Some Be Broadband customers hit back by claiming they would take their "business elsewhere".
Dunno quite how to break this to you, but unless you are planning to emigrate, you are going to discover finding a UK ISP that hasn't (or isn't about to) block TPB is a little tricky.
1) Emigrate as previously mentioned (not a bad option to be honest!)
3) Use a private tracker that's kept its head down.
4) Wait 5 minutes for a different, unblocked domain/IP to appear. Use it for 6 months whilst the wheels of the court go round and round. Once blocked, wait another 5 minutes. Repeat until Music industry resort to using contract killings on pirates with HM Govt blessing.
Changing from one UK ISP to another will not have the slightest influence on the above, except BT moving at their typical glacial speed is actually a slightly beneficial to the end user just this once!