Originally Posted by
Ldnn1
Are you aware that getting from DLR to District line involves either a nasty change at Bank/Monument or an outside walk from Tower Gateway to Tower Hill?
You can instead get the DLR to Canning Town, easy change there to Jubilee line, then change at Green Park to Piccadily. There's a bit of a wak at Green Park but it's step free.
I would do something like:
DLR -> Canary Wharf -> Jubilee Line -> Baker St -> Bakerloo Line -> Paddington -> Heathrow Express or Connect. It looks more complex but it's all luggage friendly and no stair that I can think of. Canning town may be the same effort as Canary Wharf, but I've not had the pleasure.
If you buy Heathrow Express Tickets well in advance it can be as low as £14 pp.
If you must use the Picadilly line, Green Park is probably the best interchange but there is hike between the lines within the station.
Bank is not luggage friendly at all.