I wouldn't and I personally don't. I'm also from London and have spent much of the last 10 years in Saigon and Taipei. Also Hong Kong, Bangkok and Japan. This kind of thing is always at the back of my mind.
Of course people will tell you to seek the advice of a doctor rather than rely on advice from an internet forum - but no harm in doing both, in my opinion.
Bear in mind that whether you do, or whether you don't, there are other risks concerned with mosquitos. Dengue fever is a growing problem in the region and the symptoms can be mistaken for malaria. Also a chap I know almost died following complications following a simple infection from a mosquito bite. So if you do find yourself staying somewhere with mosquitos then try to get a net / take other precautions. Frankly most "nice" hotels seem sufficiently sealed for it not to be an issue.
Its widely assumed mosquitos are not a problem in cities. Well I've had a serious problem with them here in Taipei recently - so there are no guarantees you won't be troubled even if confining yourself to cities.