"three rules" - as a bowler-hatted pin-striped carnation-buttonholed bicycle-clipped city gent many (*) years ago, I rode my Brompton in rush-hour, at a time when there might only have been one or two of them on the train unlike the "a couple stashed at every door" nowadays, from Euston to various parts of that curious city. I distilled the experience into "all the different transport types (bike, taxi, lorry etc) hate each other but at least they understand each other". In over ten years of biking the only 'serious' problems I had were pedestrians stepping off the pavement into my path. I actually FAR prefer riding in London than my own town, where "all the different transport types don't hate each other but neither do they understand each other". I'd much rather be hated and understood than the other way round.............
"ride in the middle of any lane and never hug the left kerb" - TBH, I'd plonk that in as Rule #1...
Ride idea? Bike up the river embankment to, er, well, Embankment; then back on the Thames Clipper. Did that a while ago, in reverse. The boat trip was better than any fairground ride.... pootled along like a super-annuated barge until Tower Bridge, then the cap'n pressed the big RED button and opened her up and it was unbelievable, insane even - the machine must have been rocket-propelled, the banks were a blur all the way to Greenwich. Amazing value for the price of a Travelcard or whatever it is. Apparently there's talk of extending the route to Barking but it might not be ready in time for your jaunt

. (edit: Wotsits posted as I was adding this - 2 recommendations then

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Reg (Seat 23, rear coach, Mon-Fri 08.05 Leighton Buzzard - Euston)
(*) many