What are you looking for in a dog? It can influence the preferred breed, although I would agree that retired greyhounds are a good choice unless you or your neighbours have cats - because the greyhound is one of the few breeds that can pretty well guarantee to catch a fleeing cat - others being saluki borzoi maybe deerhound and others of the larger gazehounds.

The various UK breed rescues are mostly quite reputable.

I am concerned at the practice of many of the big rehoming centres, particularly the RSPCA in castrating all dogs before rehoming. I am aware of a case in which the RSPCA castrated the ONLY two white male Pharoahhounds in the country because of this policy: a material loss to the genepool. White is permissible in Pharoahhounds, it's not like removing Dudley boxers or white GSDs from the genepool