Interestingly I lived somewhat near sizewell in the past you would be surprised in effect how little evidence of police there is.
Although the ones there are armed, you hardly saw any.
There probably isn't really that many there in reality.
I suspect getting access to the site would be relatively easy (although likely detected, so what you gonna do now type scenario). But getting access to anything sensitive would be significantly harder. Much like my local airbases who seem to have very similar levels of perimeter defence etc
Edit to add, I believe the police on the site were external to the local police as well. The nuclear police maybe?
Having gone through the process of legitimately gaining access to Sellafield, I can assure that the process is rigorous and lengthy.
Also on one occasion a colleague and I having gained access to the site and wearing our passes had a slack period and decided to take the tourist bus tour. We were quickly identified and hauled off the bus with a stern talking to.
The police are indeed seperate to the county police force and take no prisoners. They are routinely armed and trained on the in house range facility.