Assuming you don't need the chimney for a fire.
Leave the birds alone you cruel barsteward!
Assuming you need a cowl to stop the rain causing damp - the birds should be leaving the nest for winter if not already (someone correct me if wrong) so please wait til they do. Then whoever puts the cowl on should be able to lift out the nest - no?
Oh and you're just not looking hard enough for
www.chimneysweep.org/forum 