Applications to local councils for housing benefit and council tax rebate, housing or homelessness assistance require proof of identity and eligibility. For some applications proof is required about other people in the household as well. This also applies (but only in England) where 'right to rent' checks need to be made on applicants for tenancies and other adult household members (either by private landlords or, in some cases, by housing associations).
The UK has no national identity card system. Some foreign nationals must apply for biometric residence permits (also called identity cards) which include details of their immigration status and the the Home Office publishes a list of these. These cards provide evidence of identity but many of the people who have them will not be eligible for housing or benefits.
People who have got refugee status, humanitarian protection or discretionary leave get an Immigration Status Document that provides proof of identity and eligibility.
Other foreign nationals, including, for example, people who got indefinite leave to remain before the residence permits came into force, do not need identity cards. Like UK nationals, they can use any secure document like a driving licence or passport to prove their identity.
Proof of eligibility is provided by UKBA documents: these include stamps and stickers in passports, letters and permits.
Proof of EEA citizenship is provided by passports or national identity cards. A permit may prove a right to reside, but only certain family members of EEA nationals actually need them in the UK (for more on this click here for England and Wales and here for Scotland). Otherwise the proof of the right to reside is in the evidence of work, study, etc needed to acquire the relevant right.
Samples of most types of documents can be found on two websites: