Using a push bike in London is a great way to get around. The traffic is so bad, especially in London that it makes sense for you to try biking.
If you are a tourist there are many different options available to you. One of the options is to use the “Boris Bikes” which can be hired across the city. These can be hired for 30 minutes (for free) or for longer periods for a small charge. You will have to apply to get a key for the bikes, so if this is something you want to do then plan ahead for this.
There are also many cycling tours that you can do. This allows you to get around the city and see places that you might not see via bus or on foot. It also allows you to travel longer distances faster. If you want to look at some tours, have a look here.
As with any big city, watch out for bike thieves and make sure you have a good bike lock and bike equipment.