The leaving of luggage in London is not as popular as it used to be on account of risks imposed by terrorism.
That said, stringent measures have been applied to tighten up security and nowadays it is possible to find left luggage facilities in most public places, including railways stations, airports, museums and the like.
The places to be careful about are public attractions, pubs, restaurants and Government offices, which are often not equipped, nor have the space to handle left luggage. It is unlikely that you will want to take luggage to those sorts of places anyway.
If you lose some or, God forefend, all your property somewhere in London, try to remain calm and think of the statistics about how often property is (a) not lost all, or (b) frequently recovered. There is a world of difference between lost and stolen property and much of the former is not reclaimed because the owners mistakenly assumed it would never be found.
Go to where you think you mislaid whatever is lost and have a good hunt around. Speak to the people there, get them on your side. If that fails go to the Police who, if nothing else will give you a case number which will help your insurance claim.
There are around 12,000 cabs in San Diego. I once left a vitally important brief case in the boot of one after it had taken me from the Airport to my Hotel. Back at the Airport I started at the top end of the queue and the fifth cab down contained my brief case.
Nil desperandum!