Which boat, which pier, what it costs, and Greenwich at the end of it.

The Thames is the best way to see London's set pieces in order: Westminster, the Eye, the South Bank, St Paul's, the Globe, Tower Bridge, Canary Wharf, Greenwich. The trick is knowing which boat: the commuter service is cheaper and faster than the sightseeing cruise, and it stops everywhere you want to get off.
Board at Westminster for Parliament and the Eye, then Embankment, the South Bank and the Festival Hall, Blackfriars for St Paul's above the Millennium Bridge, Bankside for the Globe and Tate Modern, London Bridge for Borough Market, then under Tower Bridge with the Tower on the left, past Wapping and Canary Wharf to Greenwich. Coming back at dusk on a Friday in autumn is the best £9 in London.
Get off at Greenwich Pier: the Cutty Sark is at the top of the ramp, Greenwich Market two minutes on, the Old Royal Naval College and the Painted Hall beyond, and the climb to the Observatory and the Meridian line for the view back over Canary Wharf. Lunch at the market, boat back, four hours total. If you are staying east or going on to London City Airport, a fixed-fare car from Greenwich is 15 minutes.
The Uber Boat by Thames Clippers from Westminster or Embankment to Greenwich (about 40 minutes, contactless, from £9) is the best value; City Cruises and the Thames RIB are the tourist options; the Tate Boat links the two Tates.
Yes, on Uber Boat by Thames Clippers, with a discount for Travelcard holders. Not on the sightseeing cruises.
For the view at night, yes; for the food, rarely. Bateaux London and City Cruises run them from Embankment; two to three hours, from about £95.
Uber Boat from any central pier to Greenwich Pier, 40 to 60 minutes, then the Cutty Sark, market, Maritime Museum and the park are all on foot.
Terminal confirmed from your flight number, pickup timed backwards from check-in or tracked forward from landing, name board standing where you exit — London's entire airport system run the way it should have always worked. Sixty seconds books any of it.
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