Ntl is fine, but it is a cable tv provider - this means you get generally good broadband (all ISP have their problems) but have to use their other services. They are currently upgrading their packages so best to visit the home page for info:
http://www.ntl.com/
They have recently merges with telewest (another cable operator) and the group has bought virgin mobile. You will have to check if they cover the area you are moving to.
They advertise as 'unlimited' and it basically is, although there is a small part in the contract which allows them to curb your usage (but I've never heard of this happening, and would expect it only to happen for very high usage), and they do not block P2P usage. Oh and BTW in the UK I am pretty sure any authortity needs a UK Court order to get your details from any ISP.
Here is a useful site to check what Broadband is available in the area you are moving to:

http://www.broadbandchecker.co.uk/

There is a pop-up so best use Firefox, you will need to know the postal code for the address you are moving to.

Hope that helps