Not sure about the "official" rules, but it seems to me that as long as you aren't hoping to come back to the UK very soon on another visa (or apply for another visa) they probably won't know if you stay on a bit. But that's purely my uneducated opinion!
I personally wouldn't risk going out of the country and coming back so quickly, but I have heard of it being done successfully! In which case, you'd have up to 6 months before you weren't 'legal'.
I guess as long as you've got the funds to support yourself for the time you want to tour around, and as long as you can prove that you do intend to leave after 2 months, they probably will be fine with it.