Unfortunately London suffered for many years under the threat of terrorism from just across the water to the west of England, Wales and Scotland. As a result of that, many buildings in London were destroyed by bombs and many lives were lost.
As a result of that London is very security conscious. That's why you regularly hear announcements at tube, bus, and train stations warning that luggage must remain with you at all times and that unaccompanied luggage may be removed by the security forces and destroyed with no warning.
So left luggage, as it is called in the UK, storage places are rare and expensive. Any luggage left has to be left with a company, there are no lockers available to the public. The company will x-ray all received packages and luggage, and perform other non-disclosed tests, before accepting them.
The easiest to find places are at some of the biggest mainline train stations such as Euston, Victoria, Paddington and Waterloo.
The company who have the franchise are called Excess Baggage and their website is at http://www.left-baggage.co.uk/locations.php Before you click through, prepare yourself for sticker shock.
Many hotels will hold luggage for guests for a few hours before check in or after check out.