I think it may be more in the RSPCA's remit to help people with vet bills in an emergency. But if there is no-one to help, and the choice is PTS or help with costs, some CP branches do help (providing they have the funds to do so).
As I say we are lucky that a RSPCA hospital is near, so that is always an option for people as well, as they do not put any postcode restrictions on who they will see.
I have been in my vets when a seriously injured/ill pet has come in and the vets have rung the hospital to see if they will treat the pet as the owner is unable to afford the costs to treat at a private vets. Suppose the same applies with PDSA and Blue Cross.