I have lived my whole life in and around London. I would never attempt to 'walk' around central London carrying an expensive (or eye-catching) camera...it will probably attract security police quite quickly via CCTV which is the most of any European city...if it's not the police then it will unhappily be the huge army of foreign thieves who will quickly see you as a target.
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With respect, as you have never attempted to photograph in central London your comments are just conjecture.
I have spent 40 years, day in day out, photographing architecture and locations in London. I always use a tripod, usually with MF cameras and often work alone. I have never been robbed and nobody (foreign or British) has ever tried to rob me. I guess that a few photographers over these 40 years will have had their cameras nicked so maybe I and all my photographer friends have just been lucky....
Over the years I have had the odd low level run in with drunks and junkies but nothing serious.
Regarding Police and security guards.
In the aftermath of the 2007 bombings in London the Met Police introduced a policy of questioning photographers on the streets. As you can imagine every day there are thousands of people taking photos in London so they mainly concentrated on photographers using tripods. Their MO was to ask you what you were photographing and why and then issue a Stop & Search form which acted as a day permit. In my experience the police were often embarrassed by the stupidity of this policy but they were always polite and friendly. After around 3 years photographers had had enough and there was a large demo in Trafalgar Square.
The police, God Bless them, immediately dropped this practice and things would have returned to normal but...
Post 2007 the police had spoken to the security guards and maintenance staff of London's larger buildings and had informed them that they were the police's eyes and ears on the ground. A role that they zealously embraced and again mainly tripod users, were and still are, targeted.
Unfortunately the police never got around to telling the security community of their new light touch policy. So over the years I have honed my response to their questions and requests for ID to "If you have reason to believe that you a witnessing an act of terror you should phone the police." Repeating as necessary into it sinks in.
Eventually it works and with their pride slightly wounded they return into their building. Occasionally they will phone the cops for guidance.
However your main risk of running into security is on all the land in London that looks like public land but is in fact owned or leased by private companies. Just a few examples: Anywhere in Docklands.(it is like a city within a city. Think of the Vatican in Rome only here the god is money.) All the road leading to Tower Bridge, all the river front south and west of said bridge. Paternoster Square by St Paul's. New Street Square in the City. The bottom half of Trafalgar Square (but not the top half) All the main parks in London are owned and run by the City of London who charge for professional photography. Again your tripod will draw their attention.
Frank, if you are prepared to pay for a photo tour I would propose that you spend your money on a freelance assistant and tell him or her the sort of stuff you like to shoot in advance and between you both you can work out a plan. He can even carry the gear..
Your biggest danger in London will be looking the wrong way when you cross the road..
Enjoy your trip!
Paul
