In message , at 20:00:38 on Thu, 27 Feb
2014, " remarked:
You could change from the Piccadilly at Earls Court then get the
District line to the other station at Paddington.

That's an awkward change (tube to subsurface), especially with luggage,
but in the current weather it might be better to change to the District
at Hammersmith (cross platform as both are above ground still) then
change again at Earls Court for an Edgware Rd (not High Street Ken) train.

Is there a cross-platform change at High Street Kensington for Edgware Road?

No, but it would be stepless.
--
Roland Perry