Have you had a word with any other neighbours? If you could find out who it is, half the problem could be solved. The guilty could inadvertantly be encouraging more than just the pigeons(e.g.rats), so it could be seen as an environmental problem. Although, I'm not too sure about that.
Why not have a word with someone e.g. streetscene at the council, before the problem gets out of hand as below?http://www.bbc.co.uk/news/uk-england-wiltshire-16488207