Gulls are protected, so I doubt it. It's pretty simple, really. All householders and businesses have to do is to stop letting them nest in their chimneys, on ledges, on rooftops, etc., and as far as pigeons are concerned, there's a very tall block of flats here, which hosts nesting peregrine falcons every year. They consume a good number of pigeons, so it's sometimes a matter of a little ingenuity to reduce their numbers.
By the way, for non-twitchers, pigeons breed all year round, so there's no 'breeding season'. A small yard at the side of our flats here produces between ten to twenty per year, but there's no way to get it stopped because the Council won't interfere, it says, with the right of freeholders to do what they like with their own property. Plus, no-one seems to know who owns the tiny yard, so the pigeons carry on producing two to four squabs at a time.