My default option when there is nothing veggie specific is to eat some place Indian. Plenty of Indian restaurants do understand that vegetarianism is the way even if they do have dead animal dishes on the menu for those encultured from an early age to eat 'meat'. It would be helpful if the best Indian restaurants were on the list too.
One thing that does surprise me about the few vegetarian restaurants that are in London is the clientele. Places like Mildreds are packed night after night, and the punters seem that bit more vibrant, healthy, better looking, articulate and youthful than you would normally expect to find when eating out.
More generally, I think that something has to change regarding vegetarianism in London, much like how things have changed regarding cycling in London. As a society we cannot go on eating variants of endangered species on toast for every meal, it is just not on or necessary. Meat eaters need to lighten up a bit and put some variety into their diet.
Why can't the variety of vegetarian cuisine in London be a tourist attraction? Why can't house prices be that bit higher just because they are in an area where there is an excellent choice of vegetarian restaurants? (In the same way that being on a bicycle route adds to the value of a property.) Why can't we have some version of the 'Bake Off' on TV that is about vegetarian food, to celebrate it rather than be all preachy about how evil the meat industry is? Aside from Hitler, why is it that nobody knows of anyone famous for being vegetarian? This is particularly weird when so many celebrities, athletes, respected thinkers and others that people aspire to and respect are actually vegetarian. Where is the 'Boris' or 'Jamie Oliver' of the vegetarian cause?
Going back to the cycling situation we have had a culture shift in cycling and attitudes towards it that has not pissed off motorists. Even if they don't cycle they don't get uppity about those that do. We need something along the same lines for vegetarianism in London.
Anyway, I hope you too have ideas on how attitudes towards vegetarianism could change in London, it would be great if you could say so on your site.