The best bet is the local Natural History Groups. They will produce an annual report and if you can find one of these (the library is a good place to look) you will see the name of the local recorder and a list of contributors who will be able to give you the local details you require. It used to to be called the Cumbrian Bird Report or The Birds of Cumbria in the days when I was more active, but it may well have changed since then.