Puppy Care & Kitty Care were produced by Hornby in 1985. They were a series of plastic dogs and cats with twistable heads and brushable hair. There were lots of different poses and colours, and each one came with a comb, collar and an accessory which they could hold in their mouths via a small hole. There was also several sets of fashion for them.
Images on this page thanks to Petra, Jana & Francesca!
There were twelve puppies (more adult in shape than puppy) listed on the back of the packaging, but I have also found some more. Each one came with a bone, pipe or slipper which they could hold in their mouths, collar, ribbon and comb. There were four poses.
These puppies doesn't match any of the ones above, so maybe there was another set produced.