I'm finding this fascinating. I always say excuse me. I cant see what could be cheeky or not nice about it.
Ricki, imagine someone trying to walk past you quickly and barging into you, without comment and carrying on, the Brit use of "excuse ME!" is to indicate to that person that they are in the wrong and should have said "excuse me (neutrally of course) to you to politely request that you move.
If I cannot get past someone as a Brit, I say "excuse me" or "can I just get past you" and then "thanks" when they move.
Sorry is a bit more complicated, sorry is for when you have bumped into someone and it seems that the bumper say sorry and sometimes the bumpee also says sorry, just in case they were at fault without realising it! (this keeps everyone happy)!
Just to complicate matters, I always say "you're welcome" if someone thanks me for something, but sometimes, if someone has pushed past me, or left me holding a door open for them without saying thanks I will often say it then too sarcastically, "oh you are WELCOME"
and smile. It's amazing how many times that prompts a "sorry" and a "thank you"....... complicated - us? never!