Ahh, just realized this was an old thread…but will add my two-cents for future browsers:
I’m an American and they not only questioned me, but detained me for three and a half hours and then ultimately didn’t let me in. And I know another nomadic American that had the same issue.
I agree with everyone above, definitely don’t mention working (and keep in mind that any sort of volunteering, housesitting, pet-sitting, etc. is considered work).
In my case, after being detained, they did ask for proof of funds (which I did not have on me). So this is an excellent question. I normally wouldn’t advise people to travel with bank statements, but going into the UK it might be a good idea to have a statement on you.