I would scrub the cab option personally...
DLR to one of the Jubilee line stations, Jubilee line to Green Park then onto the Piccadilly line to LHR. More than enough time if your flight arrived from IBZ on time...
The cab will take a while to get to Paddington, you could be 2/3 of the way there by the time you were nearing Paddington, and for a fraction of the price.