A slighly old but good article about police using bicycles from the Standard.
I'd always thought that cycle-mounted police made a lot of sense. In a car you are somewhat isolated from your surroundings. On a bike, you're a lot more connected to your environment: you see and hear a lot more, and you're a lot more connected to the local population. It's a lot easier to flag down a cyclist than a police car. People get a sense of security from police 'walking the beat' because they're approachable; this must also be the case for police on bikes, but a bike is a lot more mobile.
As the article says, a cycle is also a faster way of getting around central London than a car, and there's a lot fewer places you cannot go.
Cycles are also a lot cheaper to buy and run than cars. With the looming spending cuts, maybe police will increase the number of cycle-mounted officers? I hope so because then maybe the police will start to better understand what cyclists have to put up with from other road users, and start to enforce traffic law from that perspective. Maybe motorists will start to give me a bit more room and consideration, especially if I can figure out how to look more like the cop in the picture.