Go to a Cats Protection League home if you can find one near you. They not only take in and re-home strays and unwanted kittens but also take in cats that the owners can no longer look after, for example an elderly person having to go into a care home. They encourage visitors to go amongst these cats and play with them. Granted they won't be kittens but they are just as soothing to pet, even more so as they sit still longer. I'm not sure but they might even let you play with the babies if they have any in at that time.