If you type "walk" into the app search bar it brings up quite a few walking apps. Not sure if any are designed for what your after. The other option for public footpaths would be to go to your local council website and take a look at public footpaths. The council usually have a map that highlights these.
Other than that I have no idea. Public footpath app would be quite hard to do with there being so many and possibly the limitations on what can be done by council restrictions.
Thanks for your reply... Haven't had much luck searching... There is an OS app but the feedback sounds like its an expensive POS...... Poor quality JPEG and so expensive the add in purchases would pay for a local guide