Has Samsung UK refused the repair ?
If so it's more probably because it's an imported phone so they won't provide support for it.
I used WondaMobile to import my N20 Ultra Snapdragon version and they apply a 12 month warranty and repair service but I'd need to send it back to them in Hong Kong.
This is also why I've covered my phone's through my Home Contents Insurance.
Is the screen badly damaged ? I ask because if it's minor and the screen works etc then a screen protector from Whitestone Dome can help to protect the screen from further damage.
A Standalone shop that advertises they repair phone's may replace the screen but this could in some cases result in an inferior display panel being used, further issues caused from the repair process and any warranty being invalidated.
Current Phone ~
Samsung Note 20 Ultra 5G SM-N9860_256Gb SnapDragon 865+
Samsung One Ui 3.1/ Android 11.