Shopify does not currently support the transfer of ".co.uk" domains, or other regional domains. Attempting to transfer this type of domain will result in your domain being stuck in "limbo" and may result in losing the domain. You will want to keep your domain with your existing domain provider and update your DNS records to point towards Shopify. You can do this by creating an "A" record that points to 18.104.22.168, and a CNAME record that points to shops.myshopify.com. More information on the required DNS values can be found in our help centre here.
Once you have applied the changes, it can take up to 24 hours to take effect.