Having lived in both cities, I can't help but compare them. Capitals of two islands countries where people drive on the left and are known for their politeness (or hypocrisy), both have a similar population (centre/+suburbs 8/11 million for Tokyo and 7/12 million for London). It is difficult to say which one I prefer as both have their advantages and inconvenients. Here is a short summary.
London (4/5) : Legendary underground and doubledeckers. It has more atmosphere than almost anywhere else. Even the taxis are part of the decor. Some trains and buses are a bit old though. London taxi drivers are famous around the world for knowing every nooks and crannies of their city.
Tokyo (3/5) : Clean, bright and spacious trains/metro, but buses tend to be too small (and too low for tall people), too few (once every 15-20min, as opposed to 3-8 min in London), too slow (no bus lane like in London) and often late. One more thing, there are no night buses in Tokyo. Taxis are overpriced and don't know their way around.
London (4/5) : Lots of big and beautiful parks, lots of "wooded squares"
Tokyo (3/5) : Parks are less beautiful and smaller than in London, but there are a few nice traditional gardens.
London (3/5) : Reasonably clean and wide, except in some areas. Still too much traffic even after the new congestion tax.
Tokyo (5/5) : Cleaner and wider pavements than London. Quiet residential backstreets and few traffic jams on big avenues.
London (5/5) : Central London is as good as it gets for architectural beauty. No place in the world can rival Westminster, St James, Regent Street or the core of the City. The suburbs can be ugly though.
Tokyo (2/5) : Apart from a few nice skyscrapers built recently in Shiodome and around Otemachi, and those of West Shinjuku, most of the city is an architectural chaos of concrete only worsened by electric lines and cheap plastic and neons signs.
London (4/5) : With the avent of "new British" food and all can of food the world can offer, London is (surprisingly to some) a paradise for gourmets. The main drawback are the prices to pay for good food, much too high compared to Tokyo. Indian food is especially great.
Tokyo (4/5) : One of the city's claim of fame is the quality of its food, especially Japanese, Korean and Italian (French is variable). Chinese food is not as good as in Europe though, and can be overpriced. It's sometime hard to find other ethnic food, even Mexican, Turkish or Indian. The big plus are the cheap bento and "Japanese fastfood" chains (tendon, ramen, udon, soba, gyudon, karee, etc.)
London (4/5) : A capital of fashion in itself. Great for boutiques, chains and luxury department stores (no need to introduce Harrods or Selfridges anymore). Not so good when it comes to electronic.
Tokyo (4/5) : Excellent for electronics and brand clothes. Full of department stores. Foreign brand clothes are however overpriced compared to the US and Europe. Everyday imported food (cheese, wine, chocolates, jam, cereals...) is also overpriced and can be hard to find outside specialised shops.
London (3/5) : Too cloudy and rainy, but not that bad. Winters not much colder than Tokyo eventhough London is 2000 km more north. Pleasant summer.
Tokyo (3/5) : Too hot, humid and rainy in summer with numerous typhoons. Mild and dry season (Nov-March) is not bad. The humidity makes it always feel too hot or too cold almost anytime of the year.
Safety & discrimination
London (4/5) : Very safe, although many not as much as Tokyo for petty crimes. Little racism and discrimination considering the huge ethnic mix-up.
Tokyo (4/5) : Very safe city apart from some yakuza activity. Risk of earthquakes. Rampant discrimination against women at work and sometimes against foreigners (esp. real estate companies and the police).
London (3/5) : Too overpriced at the moment, but great buildings in some central districts. Wins for beauty and quality but not price. The suburbs are still mostly ugly.
Tokyo (3/5) : Much cheaper than 15 years ago, but constructions are usually poor quality, typically with no insulation and no central heating. New "mansions" are getting a bit better though. The "reikin" system (key money) in addition to the deposit is hard to accept.
London : 34/45
Tokyo : 31/45