Chinese are very rarely seen in pet shops these days and the last time I saw one in a pet shop was early 2016 when I got Jess. The company I bought her from were taken over not long afterwards and their business model does not include the sale of any dwarf hamsters.
I have been told two different stories as to why pet shops don't sell them. One is based on demand and there is generally less demand for Chinese Hamsters than there is for Syrians or Russians and since retailers generally prefer to stock what sells best, they would rather use the extra space for more of the hamsters that do sell. Consequently as there are very few Chinese Hamsters being sold, there are less being returned to pet shops for adoption.
The second reason is because retailers themselves are selling Chinese Hamsters as they would Russians and Roborovskis and telling people that they are happy to live in pairs when this tends not to be the case and many Chinese sold in pairs will need to be split up. Upon finding that their hamsters have been fighting, people return at least one of the pair to the pet shop because they don't have the space for two cages. When my first two Chinese fell out several years ago, I told them so that they were aware of the issues and they automatically offered to pay for the second cage if I was happy to keep both the hamsters which suggested to me that it's something they'd seen a few times. Not long after I got my first two Chinese from Pets at Home, they stopped selling them in my local stores.
Knowing that it was getting harder to find Chinese Hamsters in pet shops back in 2014,I started to research breeders as I wanted to carry on keeping Chinese. I welcomed home my first Chinese from a breeder back in 2015. With the exception of Jess, who came from a pet shop in a moment of temptation, all of my Chinese since 2015 have been from breeders or have been bred by me personally.
There are a few breeders in the more Southern end of the UK, most will operate a wating list but it may be worth contacting them to find out how long their wait times are.
Vectis Hamstery (Based in Hampshire):
Vectis Hamstery and Exotics
Willow Tree Hamstery (based in West Midlands):
About Willow Tree
Lilliput Hams (based in Warwickshire):
http://lilliput9.wixsite.com/lilliputhams
Rio Hams (based in Staffordshire):
https://riohamshamstery.wordpress.com/
Metallica Hamstery (based in West Wiltshire):
Metallica Hamstery – Breeder/Exhibitor of Chinese Hamsters