No I dont think it can entirely, but depends what you intend doing. If you are going out to sleep in your hammock or under a tarp make a small fire and do a bit of cooking then you could probably get away with just a knife (maybe 4-5" blade). If on the other hand you want the fire to keep you warm as well you will need a lot more wood so a saw or axe (possibly both) would make your life easier. If you intend building shelters, making seats etc then definately a saw & axe is needed.
Personally If I had to choose 2 of them I would opt for a knife and axe and leave the saw at home. But I normally carry all 3 of them.
I get the impression that you dont currently have an axe ?? Try and see if you can borrow a friends axe to see how you get on with it before taking the plunge and spending £60 on something that you may not use a lot.
I'm still trying to understand why an axe needs to cost 60 pounds? I have one full sized Collins single bit axe, one Plumb hatchet, two hand forged tommahawks; none of which cost over $20; the tommahawks less than $15. Also two full size Plumb axe heads (one of which is a double bit) for restoration projects, niether of which cost more than $25 including postage.