If the UK was to put all people arriving from Denmark into Govt controlled quarantine, I would expect other countries in Europe to be taking similiar actions.
AFAIK, neither Sweden nor Germany as Denmark's immediate neighbours are taking special action with regards to the mink cases in Denmark. I cannot see other countries in Europe changing their policy towards travellers from Denmark especially because of the mink farms - ie the UK seems to already be much more strict on this issue than countries in the EU. Other countries in Europe seem content for the Danes to manage the response on the basis that Denmark is relatively transparent (corruption is low) and seems to show determination to get this under control
The UK alone significantly increasing its policy response and imposing a lock-everyone-up policy is unlikely to save the effectiveness of any new vaccine