Welcome to the forums, Gull. The legal ins and outs of gull nest - or chick, heaven forbid - removal are quite complex, and the fact that the law is different for the two regular roof nesting species, the herring and lesser black-backed gull, whose chicks look practically identical, makes it even more difficult to 'do' anything about roof-nesting gulls and being certain that the actions stay within the law. Any other gull species is fully protected, and since there is no option in the law to remove their nests, correct identification of the birds is crucial.
However it sometimes looks in urban and suburban areas, gull numbers are declining in the UK - so much so that herring gull is now red-listed with somewhere around 60% population decline, and all other gull species are amber listed because of somewhat smaller but still worrying levels of population decline. Any action that prevents a bird from nesting and producing young in any one season will contribute to further declines in the species. Yes, roof-nesting gulls can be a big nuisance in some situations (more so for some people than others, which is an added complexity in the issue), but there are ways and means of preventing gulls from nesting on roofs where conflict can occur in the first place rather than allowing them to choose their nesting site and then have the nests destroyed. The best deterrent is dependent on the physical size, shape etc of the site, and advice can be sought from companies that specialise in bird deterrents, and from the local council who should also be able to advice on deterrents.
Those clauses in the Wildlife and Countryside Act that allow gull nests removed to protect public health do also stipulate that such methods can only be used if non-lethal methods have been tried and failed, and that the threat to public health is great enough to warrant such extreme action. It also needs to be pointed out that nuisance and damage to property are not legal reasons for nest removal or killing of chicks or adults. The only reason is public health, and even there, a specific one-off licence from Defra or one of the devolved environment departments is needed before lethal action can be resorted to, especially if killing of chicks and/or adult herring gulls is proposed. Anyone wanting to kill gulls of any age or remove nests needs to consult the specific terms and conditions of the Wildlife and Countryside Act licences before doing anything in order to ensure that any action taken is legal, and preferably also consulting the statutory conservation agency for further advice.