One thing that concerns me about this is that public transport is, ironically, all privatised. If a company doesn't want you on their trains with knives, they'd have a very good footing for kicking you off or not allowing you on, as the law states that with reasonable excuse, you can carry knives legally in a public place; which a train is not.
However, I think that if you DO get stopped and searched, or if there's a metal detector or the like, the best course of action is to say, before they even start searching, that you are carrying knives/axe/whatever for a camping trip. I wouldn't use the word Bushcraft. It does look a bit more suspicious when they search you as you stand and look disgruntled, and they find an axe in your bag. An example of this; my father was accompanying my step-brother to court for a custody hearing. He spotted the metal detectors and realised that he had a lock-knife in his pocket, so he took the guard aside and explained that he had the knife, and offered to put it in the glove-box of his car. The guard agreed, but did state that had the metal detector gone off and they'd searched him, he would have been detained.
Peace and happy camping