If the phone is on 'pay-as-you-go' it needn't be registered so even the phone company won't know who's using it.
If the phone is registered (or on a contract), the only people who'll have access to the owner's details are a (very) few members of the phone company's staff. The only way to access this information would be to identify, and then bribe, one of these staff. Make sure, however, that this member of staff is someone that you really like because there's a very high chance that you'll be sharing a cell together for quite some time! (IT'S STRICTLY ILLEGAL FOR ANYONE TO PASS ON THIS INFORMATION UNDER THE TERMS OF THE DATA PROTECTION ACT).
Chris