Some problems with what appears to be a slow broadband connection can actually have nothing at all to do with what comes through the phone (or cable). It's quite often a problem with either the computer or the browser that's being used.
So, before proceeding any further, check the actual speed that you're getting. (If you're already getting a decent speed then there will be nothing that BT, or any other provider, can do. The problem will be 'at your end').
Here's the official speed checker from BT Wholesale (which applies to any service sent through their cables, even when it's from a different ISP):
http://speedtest.btwholesale.com/
This speed checker is also popular
http://www.speedtest.net/
See what speeds those sites are indicating and then tell us the results.