Most wood pigeons have moved to better feeding areas either south and west where it has been a less severe winter or east to mainly arable areas where there are stubbles and early brassica crops. My brother in south Devon is seeing plenty and we saw flocks in the hundreds up in Fife last week. In November there were enormous movements along the south coast featuring,on one morning, over 150,000 birds but in spite of it being a regular event not enough is known about their movements. A google search will turn up some arguments in bird forums as to whether the birds are mainly from the continent or not! Why stock doves are still around on our barren sheep pastures will need some research but I think they are more sedentary by nature.
The cold undoubtedly has impacted on small birds and yesterday whilst cleaning out nest boxes in a near-by wood we found 2 dead wrens but they may have been underneath a number of live ones, who knows? A live bat also took advantage of a box but I couldn't see which sort as it started to move and so I exited sharpish.