Twice I have filled my bird feeders recently and both times I have had to remove them and clean them out as the birds have largely ignored what I have provided in favour, presumably, for the wild food and continued insect life that they been able to gather naturally instead.
Apart from the blackberries there have been a very good harvest of rose hips and haws, holly (above) and hawthorn berries. All if these are valuable source of food to birds and other wildlife as well as brightening up our hedges, especially now the rain is setting in!
Other pretty berries in the hedgerows at the moment are those of Black bryony (below). Be careful not to pick these when foraging as they are highly poisonous!
If you want to identify other berries in the countryside at the moment, have a look here for some clues. http://www.bto.org/sites/default/files/shared_documents/winter-thrushes-survey/associated_files/berry-identification-sheet.pdf