The UK will know with certainty that a specific stamp was used to send a specific envelope to Mullvad. (e.g., America has been logging images of every envelope that passes through its postal service for over two decades).
It would also be trivial for the UK to know:
- When and where that stamp was initially sold (and to whom, if buying online!)
- When and where an envelope bearing that stamp entered the postal system
- When and where envelopes with other stamps from the same booklet entered the postal system
Add up enough bits and you can pierce anonymity.
This is a misconception caused by the scale of surveillance today. In the old days you were right. To do this kind of tracing they'd have to assign someone to do it which takes human resources and is not infinitely scalable. So they'd only do it to people deemed interesting enough, so average Joe was safe.
Today the scope has changed completely. Everything can be correlated all the time, so it is. No suspicion or probable cause needed.
If they don't do that, if they meet the stamp along the letter's journey, they can scan the code and check which batch it's from, and there could be a database of which post office got which batch, and then it's a matter of checking that post office's purchases/security cameras.
If all stamps are indistinguishable from each other, then you could've bought the stamp months ago on the Isle of Skye and used it in London, they wouldn't be able to tell the difference.