Decide on an area. London is too large to search it all, so decide on where you want to be. This may largely be decided by your tastes and budget. Central London areas are generally more expensive than suburbs further away, but elite sought-after neighborhoods can be outrageous. Look for a subway stop within walking distance if you are planning to use public transport.
Decide on the length of the lease. If you are only staying short-term, research companies online to find out the type of properties available (see Resources below). Also, decide on the types of accommodation--whether you want to rent a room (flat share) or an entire apartment.
Check it out. If you are already in the city and planning to stay a fair amount of time, it may be worth seeing apartments first hand. Cram as many appointments as possible into your time and pay special attention to the amenities.
Be flush. In addition to the generally crazy prices of London, lease payments are a little different from the ones in the States. The entire first month's rent is required in advance and another full month acts as a security deposit. Some large leasing companies may have a lower deposit charge, but private owners will require an entire month.
Agree on any changes to the standard lease and have these in writing. The same goes for any maintenance deadlines, which you should get signed if possible. If you have problems, the Citizens Advice Bureau (see Resources) offers free legal information regarding your rights as a tenant.