The paper trail will start at the viewing, if not before.

Typically:

EPC available for viewing.
Agent's terms for renting include a clear breakdown of costs that the prospective tenant will incur.

For prospective tenants (and guarantors), as is applicable:

Agency application form/s in plain English with the offer of help to complete if needed. This will likely ask the questions for the reference process and credit check, and request the information the agent will need to verify. Commonly, the application can be completed online.
Proof of age and ID. This should be a photo ID, which should be copied and verified for all intended adult occupiers.
Visa/work permit, if required, ideally valid beyond the proposed tenancy term.
Offer of tenancy letter and guarantor request.
Draft tenancy agreement for all adult occupiers, guarantors, and guarantor terms and conditions.
Inventory and Schedule of Condition.
Appliance safety sheets/info for all electrical appliances and smoke detectors.
Gas Safety Record if appropriate.
Electrical safety report.
Deposit Prescribed Information and scheme information for any deposit taken.
How to Rent Guide.
Move-in pack to include information about the agency services around repairs and emergencies, consents, as well as relevant information about living at the property and operating heating and so on, refuse/recycling arrangements. The agent's expectations when the tenancy ends should be expressed at the outset. Some agents include a simple explanation of the main tenancy agreement terms in the move-in pack.

Paperwork With the Tenant