Ted here from Shopify, thanks for posting your query!
If you have entered a UK address into the Settings > General section of your store, however, you can't see Shopify Payments listed in the Settings > Payment Providers section of your admin - it's likely that the products you're selling can not be sold using Shopify Payments. You are more than welcome to use Shopify itself but you would just need to choose a different gateway if this is this case. A list of prohibited products for Shopify Payments can be found here if you would like to take a closer look.
Would you be able to share your store's URL with me here and I'll take a look at the store?
Thanks for sharing that URL!
It looks like the store is selling products that are considered to be 'Pseudo pharmaceuticals' as mentioned here in our Shopify Payments Terms of Service. So this is likely why you're not able to connect to Shopify Payments. You're welcome to have the store reviewed by our Shopify Payments team though if you feel this is incorrect. To do so, please contact our support here for further assistance (Support > Contact Support in the main menu).
If there is anything else I can help you with, please let me know, I'm happy to help!