Great comments from the good folk here...... Personally though, I would be wondering how they got in the loft in the first place, so would either wait till they die in the colder weather or pay the £40 or so pounds for them, and the nest, to be taken out and obtain report as to where they coming in from....pay for firm to seal up if reasonable or do it myself if quoted something silly, otherwise you are going to have the exact same problem in the Spring.
All the best, crosspatch