This is a link to a blog that I wish I had written! I have just come across it today (5th June 2019). It begs a closer look at the route on old maps and modern satellite images.
It is on my list of tasks for the future!
I am particularly drawn by the fact that it was built at the turn of the century and had been lifted/removed by 1917 to be used on the continent as part of the war effort. Sadly, the story ended at the bottom of the sea as the ship transporting it to the continent was sunk by enemy action. 
As has kindly been pointed out to me, the most recent news about that loss can be found on TheFreeLibrary.com. 
A scheme for building this railway was suggested as early as 1860 with a bridge across the Torridge and stations at Northam, Appledore, Clovelly, Hartland and Bude. In 1866 a start was actually made on a line to run to Appledore with a branch to Westward Ho!, however soon after a full ‘first sod cutting ceremony’ by the Earl of Iddesleigh, the contractors went bankrupt and the project was abandoned. A project to create a 10 1⁄2 miles (16.9 km) branch from Abbotsham Road Station to Clovelly had also been put forward by Messrs. Molesworth and Taylor. 
Finally the Bideford, Westward Ho! & Appledore Railway was incorporated on 21 May 1896, with its Head Office address at the Electrical Federation Offices in Kingsway, London WC2. Soon after the line passed to the British Electric Traction Company (BET). It was not until 24 April 1901 that the single track line was opened as far as Northam, although the first trial train ran with a few friends of the directors in January 1901. The first train, pulled by Grenville was played off by Herr Groop’s German Band which had been hired for the season and it reached speeds of 36 mph on its inaugural run. The remaining extension to Appledore finally opened in 1908, on 1 May, costing £10,000. The railway was built in three sections, with the first being from Bideford at 0.39 km, the second from the termination of the first, being to Westward Ho!, length 6.4 km, 7.23 km, and the third being from the termination of the second, to Appledore, length 3.2 km, 3.91 km. 
The contract for construction was awarded to a Mr Charles Shadwell of Blackburn and the estimate was for £50,000. The initial outlay was £87,208 and Mr Shadwell was removed from his post on 13 December 1901. A subsequent court action proved that he did ‘wilfully default’ and judgement was given against him in 1905 for £7,500. Plans had been made for a 3 ft gauge track, however as it was hoped to connect the line with the L&SWR by a bridge over the Torridge, the line was built to a Standard Gauge specification. Gradients were severe in places, with a 1 in 47 on the Kenwith Castle to Abbotsham Road section. 
Here are a few pictures which were not included in the linked post above, all were taken at Westward Ho!Westward Ho! Station in 1908. This picture of Westward Ho! Station was taken in the very early years of operation, soon after the turn of the 20th century. A later, open view of the station platform and the station building which features more clearly in the image below. Westward Ho! Station. A similar view taken in June 2009 and available on Google Streetview. The Station Site has been extensively redeveloped. The large cream house can still be seen. The bell tower/campanile of the church which only appears behind buildings in the monochrome image can be seen on top of its church roof! The station and mock-Tudor building appear to have gone but the building behind (to the left of the church) is still in place! The Westward Ho! station site in 1969. By this time the site was in use as a bus depot/station. I can find nothing left of this scene. The area has been and continues to be extensively redeveloped.
A review of the route of the old railway seems eminently sensible. I hope that Part 2 will not be long in the making!
- http://rfbwharailway.blogspot.com, accessed on 5th June 2019.
- https://en.m.wikipedia.org/wiki/Westward_Ho!_railway_station, accessed on 5th June 2019.
- http://www.westwardhohistory.co.uk/the-railway, accessed on 5th June 2019.
- https://www.thefreelibrary.com/World+War+I+tank+engines+found+on+seabed%3B+HERITAGE%3A+Divers+plan+to…-a079367549, accessed on 6th June 2019.
Resources for further investigation, :
- Baxter, Julia & Jonathan (1980). The Bideford, Westward Ho! and Appledore railway 1901-1917. Pub. Chard. ISBN 0-9507330-1-6.
- Christie, Peter (1995). North Devon History. The Lazarus Press. ISBN 1-898546-08-8
- Garner, Rod (2008). The Bideford, Westward Ho! & Appledore Railway. Pub. Kestrel Railway Books. ISBN 978-1-905505-09-8.
- Griffith, Roger (1969). The Bideford, Westward Ho! and Appledore Railway. School project and personal communications. Bideford Museum.
- Jenkins, Stanley C. (1993). The Bideford, Westward Ho! and Appledore Railway. Pub. Oakwood Press. ISBN 0-85361-452-0.
- Kingsley, Charles (1923). Westward Ho! Pub. London.
- Stuckey, Douglas (1962). The Bideford, Westward Ho! and Appledore Railway 1901-1917. Pub. West Country Publications.
- Thomas, David St John (1973). A Regional History of the Railways of Britain, Vol.1: The Westcountry. Pub. David & Charles.