Sorry for the double post but have been thinking about this a little more. Why was the traction current off at Bromley-By-Bow? It's on a completely different traction current section...
Bromley-By-Bow is on the current section Campbell Road (Just West of Bromley-By-Bow) to Plaistow EB. East Ham is on the current section Plaistow to East Ham EB.
Although I'm not sure, I wonder if the traction current arrangements were very different at the time of this incident.
If you refer to the diagram at the end of the accident report, you will see that the District line and what was then the LTSR (now C2C of course) were still connected, and this was before the major remodelling of the District line in the late 1950's; I am not sure - I hope Tubeprune will happen across this thread as I am sure he will be able to add value.
On a more general point, the braking (and particularly in this type of circumstance) of trains is now quite different.
There are no longer the hand brake systems on current stocks, so they do not rely on being manually applied; indeed the 'holding brakes' will automatically apply as air pressure reduces; this system is the 'Spring Applied Parking Brake' (SAPB).
I can assure you from personal experience that this system works; I have had a heavily loaded, stalled train on a significant gradient where traction current has been discharged and where air has bled off. The train did not move; and furthermore could not be moved until after current had been recharged and air pressure restored. Only when the normal braking system has become enabled will the SAPB's release.
I speculate that this incident may also have been relevant of the SAPB system on later stocks (that is entirely speculation on my part).
EDIT: Reading the report seems to confirm my speculation about the supply of Traction Current; an extract from the report reads:
"The electric lines to Upminster are under the control of the Eastern Region from Campbell
Road Junction onwards, though they are used mainly by District Line and Metropolitan Line trains.
Maintenance of the track and signalling is an Eastern Region responsibility, and the signalmen and other
operating stalf also belong to the Eastern Region; the motormen and guards, however, belong to the
London Transport Executive which is also responsible for the power supply.
Tralfic is regulated from the Eastern Region control room at Fenchurch Street Station where
there are three sections, for the main line from Fenchurch Street to Shoeburyness, for the line from
Harringay Park to Pitsea via Barking and Tilbury, and for the "electric" line to Upminster. The Deputy
Chief Controller who is in charge of the room is also directly responsible for the main line, and there is
a controller for each of the other two sections. In normal circumstances the tralfic over the "electric"
section is separate from that of the other two sections, and the "electric" controller works more or less
independently of the Deputy Chief Controller. There is .a direct telephone line to the Electric Traction
control room at Heathway sub-station and another to the London Transport District Railway Control at
Leicester Square, and a series of telephone circuits between the controllers and their areas of responsibility.
It had been recognised for some time that these circuits were inadequate, particularly for the control on
the "electric" line, and a new installation had been authorised."