Yeah, I thought it was pretty stupid. If it was all happeneing right after WWIII where military resources would be hard to find locally, or that it was a post-apoc flick where it would make sense not to have a lot of hardware to defend ourselves...
Hell, if the navy (british, us, take your pic really, this is global stuff), knew where the male usually hung out specifically they could shoot some cruise missles out and level the place...
And even though it is London, if the fate of the world depended on that one dragon dieing? It'd be nuked.
Maybe only one of the babynukes they used in the old 'Atomic-Annies' but still...
(Howitzer with a 20 mile range firing nuclear ordinance...)