I agree that on any given day and depending on circumstances, you will get a different opinion from as many police officers as you can encounter in a camping trip

My own experience (at least in Scotland) is that if you are doing outdoorsy stuff with a knife or an axe (in a "proper" outdoors location, in its appropriate context and not "flashing" it, so to speak) then that is your reasonable excuse for having and using the tool in question. That includes transporting from home and back again - if it is stored out of sight and ideally located in a pocket, secondary bag or other place that does not allow immediate access, then it would be regarded as safe and proper conduct for the activity in progress (NB - lying uncovered in a car boot may not be regarded as a sufficiently suitable security precaution). I wouldn't go on to a family camp site and start chopping and cutting stuff - that is just plain daft and asking for trouble, especially if you have a small arsenal of blades at your disposal.
The Police are not looking to criminalise bushcrafty folk if they act responsibly in appropriate locations - however they do not want to allow potentially dangerous weapons to be aired in non-appropriate situations. (like don't arrive in the city with an axe strapped to the outside of your rucksack). If you stop off at the pub on the way home and insist upon showing off your edged tools (ie potential weapons) then that will drop you right in it in terms of your average police officer. Forgive me if I am stating the obvious.