You can fly whatever route you want - as long as it meets the requirements. No need to prove it either - the logbook is a legal document so has to be correct. If they don't believe you flew the cross country you claim, then they would have to call into question EVERYTHING you claim on your application. Just fill in your logbook and post it off - the CAA will look at it and then send you your blue book!
Somebody mentioned having to take on fuel at one destination - not true although flying 300nm in your C152 it might be a good idea to stop for petrol
