An assessment takes place most of the time after the initial application, but before any formal offers can be made.
This process can be fairly detailed, and usually includes a soft credit check that will not leave a mark on your credit file. Once the application progresses, this goes on to the underwriters to take a closer look.
Usually, an assessment will take anything from two to six weeks - although you can speed this up by consulting an independent broker beforehand who will be able to advise on what information is relevant.