How does the atmospheric circulation system explain the u. k.’s mild, cloudy and wet weather?

Because of its proximity to the Atlantic ocean and it latitude.

Explanation:

In the global atmospheric circulation, the UK is close to a low-pressure area where the Polar cell and Ferrel cell are meeting. This would account for a lot of clouds. This also means that wet Westerly prevailing winds blow in towards the UK, causing a lot of precipitation. However, the UK does not get the same cold extremes in the winter or hot extremes in the summer like some countries on the same latitude. This is due to the warm ocean current from the Gulf Stream. Water has a much higher specific heat capacity than land so it stays mild and helps the land around it to stay mild also.