Flip top plug stuck! Please help - any ideas!??

You could try using a small flat bladed screwdriver to prise one side up. Are you certain that it's a flip plug and not a pop up one?

A small 'suction cup' or 'dent puller' might be worth trying to give you something to pull/jiggle on.

If it's one with a rubber O ring around the flipper, you're probably wasting your time as you'll probably find the O ring is damaged and displaced and it won't ever work properly again. Plenty of bad reviews for those (not seen one in person) and probably worth having the waste replaced.

The good wastes of this design do not have, nor do they need, a rubber seal, and they do not tend to jam, in my experience. Graham plumbers merchant and BES both stock them. Cost of the part is usually less than £15 - assuming it's a basin waste (although the Wirquin ones cost 4 times that, but seem to be much the same!).