If your family is able to meet the visa requirements without your support (even if you’re providing it), a simple statement of your address in the UK, proof that where you live has adequate space for them as defined by the Housing Act, a copy of your lease agreement, and that you have permission to have visitors (from the landlord or the council).
Should your family be unable to satisfy the visa requirements without sponsorship, the guidance Immigration Rules Appendix V: visitor rules clarifies that the sponsor would have to submit all of the evidence that an applicant without sponsorship would submit.
V 4.3 A visitor’s travel, maintenance and accommodation may be provided by a third party where the decision maker is satisfied that they: (c) can and will provide support to the visitor for the intended duration of their stay.
The best explanation of that comes from the expertise of @GayotFow on Expats sister site, Travel Stack Exchange:
By can they mean that the sponsor has to demonstrate their capacity for sponsorship by submitting all of the evidence that an applicant without sponsorship would submit. This includes:
- Bank statements, salary slips, employment contracts, and anything else related to financial readiness.
- PLUS proof that there is sufficient accommodation without violating the Housing Act
- PLUS if the housing is rented or provided by the council then evidence that the sponsor has permission to take in visitors.
- PLUS evidence of care if there are children or elderly involved.
By will they mean that:
- you will collect them from the airport
- PLUS drop them off at the airport (and yes, we have refusals on those grounds in the archives here)
- PLUS provide all of the requisite maintenance and accommodation
- PLUS an attestation that you will be in the UK for the entire course of their visit.