The Carlisle to Port Carlisle Canal opened in 1823. It was approximately 11 miles long. It linked the city of Carlisle to the Solway Firth. 
Prior to the 16th century, coal from mines at Ellen Foot (now Maryport) was brought up river to Carlisle and other locations by boat. However, in 1720, duties began to be levied on all goods carried around the coast by sea.As a result, the local coal trade switched to land-based transport.
It took the actions of a small group of local traders to secure an Act of Parliament in 1721, which allowed coastal duties to be waived. While the Act enabled them to build wharves and warehouses and erect cranes, even allowing the dredging of the river and the charging of tolls (for 31 years), it did not permit them to improve the river in any way. 
The Canal was a long time in coming … a public meeting which sought its construction did not take place until 21st May 1807. “The principal aim was to provide the city with a better and cheaper supply of coal, and a committee was appointed to push the plan forwards. They asked the engineer William Chapman to advise them, and he proposed a route from Carlisle to Maryport, which he had also promoted in 1795 as part of a coast to coast route. He estimated that it would cost between £90,000 and £100,000 to build, but conceded that a terminus near Bowness on the Solway Firth would be cheaper. £40,000 would pay for a canal suitable for 45-ton boats, but a larger canal, suitable for 90-ton boats that could cross the Irish Sea or reach the Forth and Clyde Canal, would cost between £55,000 and £60,000. The larger canal could still be part of a coast to coast route. The options as to the size and destination of the canal were put to subscribers by the committee. In August 1807 Chapman suggested that a ship canal for the Irish, Scottish and Liverpool trade, and a 50-ton canal to Maryport for the coal trade could both be built, with both finding support in the newspapers.”[3: p337–339, 456]
With a range of options on the table, the Committee sought a second opinion from Thomas Telford. He produced a report on 6th February 1808.
Telford “described a Cumberland Canal, which would allow sea-going vessels to reach Carlisle, but would also be part of a grander plan to link Carlisle to other parts of the country, and could be incorporated into the coast to coast waterway. He suggested that locks should be at least as big as those on the Forth and Clyde Canal, with a width of 20 feet (6.1 m) and a depth of water of 8 feet (2.4 m) over the lock cills. His canal would leave the Solway Firth about 1 mile (1.6 km) upstream of Bowness-on-Solway to reach Carlisle, and would cost £109,393. In order to provide a water supply, a navigable feeder would continue onwards to Wigton, which would be suitable for 7-foot (2.1 m) wide narrow boats, and would cost an additional £38,139. He also quoted two other prices for narrower canals, but noted that these would require goods to be transferred to smaller boats, with the inherent costs and inconvenience.” [3: p339]
Sadly, no further progress was made at that time.
After a further eight and a half years, another meeting was held at Carlisle. The result of that meeting on 7th October 1817 was that Chapman was asked “to produce a survey for a canal suitable for vessels of at least 70 tons. He was to ensure that it could become part of the coast to coast link. His canal started at Fisher’s Cross, subsequently named Port Carlisle, … It would feature locks 74 by 17 feet (22.6 by 5.2 m), while the channel would be 50 feet (15 m) wide by 8 feet (2.4 m) deep, and would cost £75,392. A link to Newcastle-upon-Tyne could be built on a smaller scale, and another link could be built along the valley of the Eden to serve slate quarries near Ullswater. His plan was accepted, money was raised locally, and an Act of Parliament was obtained in 1819, which authorised the Carlisle Canal to raise £80,000 in capital, and an extra £40,000 if required. The chairman of the committee, Dr John Heysham, suggested they look at other canals before starting work, and visits were made to the Lancaster Canal and the Forth and Clyde Canal. [3: p339-340]
Contracts to build the entire canal were awarded by early 1820. The Canal opened in March 1823. It was “11.25 miles (18.11 km) long, had a surface width of 54 feet (16 m) and was 8 feet (2.4 m) deep. At Fisher’s Cross, a basin 250 by 80 feet (76 by 24 m) had been built, which was connected to the Solway Firth by a sea lock with a long timber jetty. Seven more locks raised the level of the canal by 46 feet (14 m), and at Carlisle there was a second basin, 450 by 100 feet (137 by 30 m), complete with wharves and a warehouse. The locks were 78 feet (24 m) long and 18.5 feet (5.6 m) wide, and water supply was provided by a reservoir on Mill Beck near Grindale.” [4: p128]
The cost of construction was just over the estimated £80,000. [3: p341]
In 1825 the Carlisle & Liverpool Steam Navigation Company paid for the construction of an exclusive berth at Port Carlisle. The Canal Cpany purchased their own packet boat to transport passenger from Port Carlisle to Carlisle. Both passenger services commenced in 1826. Goods carried from Liverpool to Port Carlisle were carried along the canal by lighters. The Solway Hotel opened in Port Carlisle soon afterwards. [3: p341-342]
Times were beginning to change. … In “August 1824, there were public meetings in Newcastle, to consider again the idea of a canal to Carlisle, or possibly a railway. William Chapman, who had surveyed a route for a canal in 1796, suggested that the route was also suitable for a railway, and was asked to cost both options. He quoted £888,000 for a canal and £252,488 for a railway. A company was created to build a railway, although they did not obtain an Act of Parliament until 1829. There was support in Carlisle, and an agreement was reached that the railway would terminate at the canal basin.” [3: p342-343]
The opening of the railway to Newcastle in the 1830s brought a significant upturn in profits on the canal. Its imminent arrival resulted in another shipowner starting a service between Carlisle, Annan and Liverpool.
“However, the boom did not last long, and the company found that it was in competition with the railways. The Lancaster and Carlisle Railway was authorised in 1844, and was a direct threat to the steamer service and canal. The Maryport and Carlisle Railway had been authorised in 1837, but opening was delayed until 1845 by financial difficulties. It was extended to Whitehaven in early 1847 by the opening of the Whitehaven Junction Railway, and at the end of the year the Lancaster and Carlisle Railway opened. The Caledonian Railway opened in February 1848, running northwards from Carlisle to Scotland.” [3: p345-346]
“In March 1852, the company decided that the best option was to convert the canal into a railway, raised some money from shareholders and loan holders, and sought an Act of Parliament. Work began in June 1853, although the Act was not obtained until 3 August. An omnibus service was used to ferry passengers between Carlisle and the steamers at Port Carlisle, and the canal closed on 1 August 1853.” [3: p347-348].
The Act both wound up the canal company and created the Port Carlisle Dock and Railway Company. Further details about the history of the Canal can be found here 
Construction was completed within a year and opened to goods traffic on 12 May 1854 and passengers on 22 June. 
The Port Carlisle Railway Company had filled in the canal basin at Carlisle and built sidings and a passenger terminal there. Passenger services between Port Carlisle and Carlisle were short-lived. Two years later the line from Carlisle to Silloth opened. The through passenger service to Port Carlisle was replaced by a horse-worked service between Drumburgh and Port Carlisle. This horse-drawn service lasted until 1914 when it was replaced by steam-power. In due course a steam railmotor service was introduced which lasted until the branch closed in 1932. 
The Route of the Line
The Port Carlisle Branch left the main Caledonian Railway line at Port Carlisle Junction, which was just to the North of the River Caldew, and curved way to the Southwest.
Wikipedia tells us that Kirkandrews-upon-Eden railway station “sat close to the village in the cut of the old canal; it had a single platform, and a shelter. … A substantial station building was present. A large seed warehouse was located at the station. In common with other stations on the line, it had its name picked out in sea shells on a raised area opposite the station building.” 
Continuing on from Kirkandrews the old line curved round to the Northwest. As can be seen on the next extract from the 6″ OS Maps of 1901, there are a couple of things which show that the old railway line followed the Carlisle Canal along most of its length.
Wikipedia tells us that Burgh-by-Sands station “sat close the village, reached by Station Road that branched off the mainstreet; it had a single platform, a shelter and a signal box. … A substantial station building was present, together with a station master’s house.” 
After passing through Dykesfield the railway broke out onto the marshes on the South side of the Solway Firth. A long straight stretch of line carried trains on to Drumburgh. The picture immediately below gives an impression of the lay of the land and shows that the railway was indeed built within the old canal.
Wikipedia informs us that Drumburgh Railway Station “was the junction station for the Port Carlisle Railway branch and the Silloth branch, serving both as a junction and transfer station and also serving the small village of Drumburgh. The station closed on 4 July 1955; nothing now remains of the station. The line to Silloth closed on 7 September 1964 as part of the Beeching cuts. Port Carlisle was two and a half miles away by train and Glasson was one and a quarter miles away. The journey time was nine minutes, although Glasson was a request stop.”  The service to Port Carlisle was horse-powered.
Griffiths and Hooper tell us that Port Carlisle had two locomotive sheds: “Firstly, a 32ft x 14ft one-road dead-end building, in brick with a tiled, pitched roof and having a central smoke vent, was erected to the east of Port Carlisle station. It stood at right angles to the station and could only be entered via 24ft turntable accessed by an approach spur; a water tank stood near the depot but it is not known what facilities were available for coal.” 
Once the steam-hauled service was replaced by the horde-drawn Dandy it seems as though “the engine shed remained in situ – assumedly it was utilised for stabling the horses and possibly also to shelter the small tramcars, but that needs confirmation.” 
A steam hauled service was reinstated on “6th April 1914 when an inaugural passenger train was run from Port Carlisle to the city of Carlisle … behind a North British Railway Drummond ‘165’ class 0-6-0T, No. 22, that engine having been taken off its previous regular duty on the Langholm branch to run the passenger service from Port Carlisle. However, less than three years after the upgrade of Port Carlisle passenger services World War I brought an economy measure whereby the branch closed to all traffic from 1 January 1917 and until reopened from 1 February 1919.” 
Griffiths and Hooper believe that the second engine shed we built not long after 1914, when a locomotive-hauled service was reinstated “or it may have appeared with the post-war reopening. It was a single road through building in wood on dwarf brick walls and with a pitched tiled roof, scaling 34ft x 16ft. It was positioned over the approach spur south of the turntable, which then, or earlier, had been reduced in size to 16ft diameter. Being of such modest dimensions it was realistically of little use anyway so it probably did not matter that engines had to pass through the shed to access the ‘table.”