Fastest route from Piccadilly Circus to Prince Regent

Option 3 or 4 would be quickest.

Surprisingly the TfL journey planner suggests via Green Park or Waterloo.

I would go via Holborn and. Bank.

I have a lot of experience of travelling between that bit of Central London and the eastern branches of the DLR. There is little difference in the timings, but via the Jubilee Line is a couple of minutes quicker and so that is the way the planner recommends (it may also have a bias in there to discourage people from adding to the congestion at Bank?).

Generally on the way to Central London I'll take the slightly quicker route and go via the Jubilee. On the way back I'll more often go for a route with fewer changes, particularly as the high level DLR platforms at Canning Town are very exposed and consequently get very cold.

No, all the Stratford International trains are too Beckton after about then, but Beckton is also served from Tower Gateway all day.

I would take the Bakerloo to Waterloo, then Jubilee to Canning Town, changing there for the DLR, as the interchange at Green Park between the Piccadilly/Victoria Lines and the Jubilee Line involves a very long walk which I try to always avoid.

However aided by the moving walkway!