My budget is around £500, but I've heard LED over plasma for gaming is better?
LED tv's do not exist they are LCD with LED backlighting.
Plasma's handle motion a lot better and up until this year had better input lagg (sony lcd's have best input lagg now from 2013 panels only).
There are advantages and disadvantages of both which some people just seem to never look at.
Plasma - cheaper, bigger, better picture quality, better motion handling and low input lagg
LCD's - no image retention issues, no reflection issues, extremely low input lagg on sony 2013 models only (otherwise plasma is usually lower).
Do Plasma screens still have a problem with screen burn?
screen burn became non existent many years ago, image retention however is still there and if you follow certain procedures it should never become a real issue.
run the tv in for the first 200-400 hours with normal useage, do not game for longer than 60 minutes a session in this time if the game has static images, etc.
use the scrolling bar after every session with a static image to look for image retention, if there is some, leave the scrolling bar running for a couple of hours, if not then continue as normal.
keep static images and black bars to a minimum or avoid completely whilst the panel is new is best.
the longer you run in the panel (use it) the more resistant it becomes to image retention, so the more the tv has varied use the more resistant they become and therefore less of an issue retention becomes.