DrRox, EasyJet (U2) doesn't fly between in/out of London-Heathrow, but it flies only four London Airports (Gatwick, Luton, Southend and Stansted).
Leg 4 started at around early afternoon on June 6 (Friday), teams are likely to fly to Copenhagen.
Loganair (LOG) 6996, LSI-EDI, 1605-1744 (scheduled 1605-1730)
British Airways (BA) 1463, EDI-LHR, 1955-2111 (scheduled 1935-2100)
Spend the night at London Heathrow Airport to find the earlier BA flight to Copenhagen
British Airways (BA) 812, LHR-CPH, 0728+1-1008+1 (scheduled 0710+1-0955+1)
This has ruled out and I agree with DrRox, see the post below for the ferry schedules.
I think Phil, Bertram and the production crew left Shetland Islands by the morning of June 6th to Copenhagen:
Loganair (LOG) 6992, LSI-EDI, 0740-1000 (scheduled 0740-0905)
British Airways (BA) 1443, EDI-LHR, 1152-1324 (scheduled 1155-1325)
British Airways (BA) 818, LHR-CPH, 1513-1800 (scheduled 1430-1720)