Employer keeps my letters from my doctor appointment

[schooling123]

When asking time off employer wants to see letter. Now they want to keep a copy of my doctors letters about appoitments. Can they do tgat? There is personal info address hospital no, clinic details etc

It's perfectly acceptable. Every company I have worked for has expected the same.
If you're worried about ID you can redact the NHS number but you'd need to leave your name as otherwise it could be anyone's letter.
As a side note though - you mention address, wouldn't your employer already have that? Unsure why that would be a concern.

Copies of these letters always goes in the employees personal file, where I work.

What is it that concerns you?

Keeping a copy seems fair enough. If there's any dispute later then the full paper trail is available.

Redact any hospital numbers, NHS number etc, as they are personally identifying and your employer has no reason to need that information.