This is pure BS
1. He says in his own site that he bases his routes on public rights of way. These are published by the Ordnance Survey and are in the public domain. Free to use by anyone constructing a route. Walking routes present themselves obviously from the map - there is no way you can check it has not been published before.
2. If you go on to websites, such as the OS mapping site or ViewRanger, you will probably find copies of his routes there too- again public domain.
3. I suspect many of his routes will have been walked by others long before him - he cannot demonstrate that invented them, nor I suspect, looking at the subject matter, can he prove he was even the first to publish them.
If you go on any walking website you will find duplicates, with or without variations of popular walks. For example, if you go on the OS site, there are often duplicate traces, with or without minor variations, of popular walks.
He can legitimately claim copyright for his narrative, his pictures and his sketch maps. To claim copyright infringement he would have to demonstrate you lifted the routes from his books. However, the truth is that you and he got your route information from a common source - the Ordnance Survey which predates both of you.