How can i find the best broadband in my area ? really need some advise

Hi guys im with BT Broadband and i pay full and only receive a speed of 516kb which sucks.

Its not my computer its brand new and expensive , ive called BT numerous times who said they where doing things and said they sent out engineer and up my speed but made no difference.

All my networking is fine all new cables short etc set up good.

I wanna switch providers but ive got no idea if this is gunna make any difference whatsoever , i cant play any online games because i get way to much lag.

If i knew a way or some SP that could offer me an average connection i'd be super delighted, if any of you guys have any ideas d be realy happy.

My postcode is S727JU if this helps.

Any reply will be really helpful. Any information you need just let me know.