I expect it's the Grey Squirrel Kenno, as this is the one most often seen. It is a bit of a nuisance but still enchanting to watch especially with babies.
The gestation period is 42-45 days and there are 2 breeding seasons, in early Spring and early Summer, each of which produces a litter of 3 or 4 kittens. Here's a bit more from the BBC Nature site:
http://www.bbc.co.uk/nature/wildfacts/factfiles/190.shtml