There used to be an RSPCA rehoming kennels in Enfield, it was a bit rough so not sure if it's still running, or there's a privately run one in Bishops Stortford called Foxdells which is Herts but on the Essex border. I'd search the internet and you'll be bound to find one.
It's also worth posting in the Homes offered board on dogpages with details of what you're looking for, including info about the family circumstances as lots of dogs are kept in foster homes and so there may be some from further afield rescues being kept in your area.
There's one on the A127. I can't remember what it is called but I think it starts with a C? Anyway, it's on the west-bound side - it's a kennels with a big 'homes needed for dogs' sort of sign outside.