I know someone who works at Freshfields, they seem to have a very good name, and as they also have a rescue in Liverpool they always have lots of dogs in need.
Many Tears have a lot of dogs in foster homes, and a fair few in the Llanelli area - I suspect that is their founder, or could be a sanctuary, not sure.
Here's some Welsh rescues http://www.dogpages.org.uk/wales.htm
Though may find more Googling as aren't all listed. There are breed/type rescue's too & if able to travel are some rescues that do home out of their local area.