I am not able to manage VAT details at this time, and so I can no longer ship to the UK.
BUT! I do have an option. Ebay!
My personal Ebay account has shipped so much playing cards over the years that I can use their international shipping program: someone buys from me, I mail it to Ebay, and they mail it to you, dealing with all of the customs stuff. And they charge and manage VAT without my involvement needed!
So I know it's a goofy work-around, but it's what we've got.
Below are (hopefully) active links to ebay listings. If there is something on my site that you want and isn't below, please get in touch! Thanks :)