If you decide to do as Barney suggests and get a clearance to cross the zone, please check your aircraft's gliding capability. Remember the requirement to be able to land clear of a built up area in case of an engine failure. You will have to turn down any clearance which is at an altitude which wouldn't allow you to do this. And since the zone only extends to 2500' (it's a class A TMA above that) it may be that it's not possible at all. Not something I'd try in a single-engined aeroplane, personally.
But there are plenty of airfields around the edge of London which will happily take GA aircraft, and you can get good views of London while remaining safely clear of the built up areas if you wait until a day when the viz is at least reasonable. Have fun!
FFF
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