I can't seem to add any cards to my wallet for Apple Pay

Though probably familiar, here’s How to use Wallet on your iPhone, iPod touch, and Apple Watch - Apple Support

Here are the details of where Apple Pay is supported: Countries and regions that support Apple Pay - Apple Support

Are you in a country or region with Apple Pay?

Reboot the iPhone, amd try again.

If there are any VPN client apps, or add-on iOS “anti-malware” apps, remove those and try again.

Failing that, back up, reset your iPhone using a Mac or Windows system, reload iOS, and restore your backup.

Failing all that, call the folks Apple Support, then.

Did you make sure your Apple ID was set to UK? Did you make sure the region on your device is set to UK also?

You are welcome.