Well if the government want information on you they can obtain it anyway. You'll never stop them this side of going completely off the grid and living in a cave somewhere which even then is pretty much impossible in the UK as we have the most CCTV cameras anywhere in the world. Even our major roads are monitored with CCTV and cameras that automatically read your number plate as you drive by, and practically every shop has CCTV to the eyeballs. You could walk everywhere but you'd never avoid the CCTV in any major area.
As for anyone else, its impossible in the UK unless you have the right connections. In the US I know you can get details from reverse look ups and credit histories etc. In the UK, all of that is illegal. We have a Data Protection Act that makes it illegal to disclose any private information about a person. In the Uk, its impossible to look up an address from a phone number or obtain other private info unless your a government agency (or you know someone in a government agency such as the police who'll do it illegally for you). The only way of finding an address is the Voting Register which is publically available but even then you need to know the name and city (and preferably the voting ward) to be able to do it and its a long process or Birth and Death Certificates.
Also, many IP's including mine are non static. So every time I restart my router I have a new IP. The best you can hope for from a UK IP is ISP details.