You must ask to see their original documents which prove they can rent a property in the UK. These documents are:
- UK passport
- EEA national passport
- EEA identity card
- EEA permanent residency card
- Biometric residence permit with unlimited leave to remain / reasonable time remaining
- UK immigration document with unlimited leave to remain / reasonable time remaining
- Passport endorsed with unlimited leave to remain / reasonable time remaining
- Certificate of naturalisation as a British citizen

You must keep copies of these documents and note when they expire if the tenant does not have indefinite leave to remain. If the tenant cannot produce new documents to show their stay has been extended then they will no longer have the right to rent and you must inform the home office.
If it is proven that you have not checked your tenants right to rent or that that you didn't follow up the checks when the permission was due to expire, you could be fined or even go to prison.