You will be asked to give references to your prospective landlord/agent to confirm your details and background.
The typical referencing criteria consists of:
Three years' address history
Landlord details for any property rented in the last three years
Confirmation of earnings, per annum, that are normally equal to the monthly rental fee, multiplied by 30
If you're retired, then your (joint) pension, per annum, will also need to equal 30 times the monthly rental
No adverse credit in the form of a county court judgement, bankruptcy order or similar
If you are self-employed, either an accountants reference or evidence on the last three years' tax returns
Most agents will ask you to complete the details of your references online. Please make sure you give plenty of contact details so that the process is quick. Its also worth speaking with your references / referees so they know they will be approached.