As a representative of Southwark Cyclists who has been involved on cycle security committees incorporating Southwark Police and Southwark Council, I have some knowledge of cycle theft, at least in Southwark, and have personally lost two bikes in recent months. Frankly, it is not "safe" to leave your bicycle anywhere in London. In Southwark, bike theft is particularly bad in SE1 and areas along the River, although this is partly due to the relatively large number of bikes parked in these areas -- Tate Modern, Borough Market, London Bridge, Surrey Quays.
153 bikes were stolen in Southwark in a two-week period. In a 12-week period, the area around Tower Bridge Road had approximately 39 bicycle thefts, eight of which were from underground car parks or garages. 40% of bicycles stolen are said to be of low value, although I don't know exactly what that means. Most bikes were locked and secured, although there has been no analysis of the quality of locks used.
Two good quality locks are better than one ("Sold Secure" rates locks on a bronze, silver and gold basis), and you should attach your frame and wheels to an immovable object where the bike is visible to passers-by if you have to leave it in the open. Leaving a bike overnight in a public place is asking for trouble. A cable (wire) lock may be okay as a second lock, but is easily cut through.
Even keeping your bike in your garden shed, or on your balcony is no protection, unless it is locked to something solid and you use good quality locks.
Registering your bike (or any other property) on www.immobilise.com may help to get it back if it is stolen.