- Not all want that responsibility, even if they don't routinely have to carry
- It's expensive to train them
Criminals rarely have guns in the UK so enforcing the law with firearms is not usually necessary.
It's traditionally been the job of the Police to uphold the law with the consent of the People.
It's the job of the Military to extend the will of the Politicians by bringing violence to enemies of the State.
By further militarising the Police, it implies the People (or sections of) have become enemies of the State, which is not a great situation to be in... also this is why a lot of British people consider US Police Departments to be insanely trigger-happy.
We have specialist armed police units for times when weapons are required, and most of the time they are not.