Are you in this situation ?
If you are unable to keep your dog then you have a duty of care to pass it on to a place that will care for it. However, it is important that you pass it to an establishment that will take care of it and ensure that it goes to a good home.
Sadly, there are some people/groups who claim to be dog or animal rescue centres, but in fact they are using dog sales to fund their lifestyle. Some so called "rescue" organisations are actually breeding from rescue dogs and selling the cross breed pups as a cash crop.
If you have a dog that is a pedigree breed, then you should contact the rescue/welfare section of that breed's national breed club. All national breed clubs have volunteers dedicated to take in and find suitable homes for the rescue dogs. "Pedigree", in this context means one of the 210 breeds recognised by the Kennel Club.
If your dog is a cross breed of dog, then you should contact Margaret Green Animal Rescue.
Their website is here www.margaretgreenanimalrescue.org.uk