I don't really think that Pret a Manger check any references or background, they just trust what everyone wrote in the c.v.
Yes they do check their previous employment reference
When I did my application at the walk in centre in Victoria station they did not ask me for any experience or references in paticular. But they where very focused on personality on the other hand. They were looking for something more in the terms of a persons motivation, determination and so on.
No, no required any references, no previous experience required for this role