The problem will be that your home telephone service is probably with TalkTalk. To change internet provider will mean moving the telephone service, too.
TalkTalk is not exactly the best provider in the UK. Despite that, I don't think I would change provider because my children's games were being cut off from the internet.
You do have the option of a standalone broadband service using 3G - for example,with GiffGaff - if you are in range of a suitable cellsite.