In reply to Dominicandave:
ALL employers are required by law to ensure that anyone they employ MUST have proof of the right to work in the UK. Obviously as an employer the first thing most ask for is a copy of your passport. If you are British or an EU National then thats accepted as proof.
It is perfectly normal to do or ask this prior to appointment and following a successful interview. A national insurance number will, in any case be required whether you are English or from China.
Most employers would simply ask you where you live. They have a right to insist on this information and I would normally simply ask people for their address, but depending on the job and industry you are in I might just ask for proof!
Would I volunteer this to an agency - rather than directly to an employer? I don't have enough experience to answer this. It may be more relevant if they are paying you directly rather than via a third party and so on. If the agency is legitimate they have a legal duty (Data Protection Act) to use the information you give them for only the purposes it is asked for and must not disclose this information to ANYONE without your express permission.