We seem to be getting a bit mixed up here. As I understand it the DC Lines, Watford and the North London, were LT-style +/- 4-rail, right through to Euston/Broad Street, which aided how the Bakerloo was extended out over it, and indeed the District running out to Richmond. This applied to the LNWR stock, and the replacing BR 1957 stock. Some time (1970?) the BR sections were converted to normal 3rd rail, with an earthed 4th rail where LT trains still shared the tracks.
The whole thing of stray earth currents does seem to be a "dark art" - at least to some. Although the DC lines had been there long term, when the 25Kv was extended in the 1980s over the North London 3rd rail, a whole series of such issues arose; in particular there were problems with the Victoria Line signalling, including blown LT fuses, where it passed well underneath at Highbury. One (well informed) electrical engineer referred the (doubtless also well informed) project engineers back to a classic electrical textbook, by Dover, published about 1914, which apparently describes just the issues they had run into.
The most surprising account I saw was from Stanford University, near San Francisco, in about 1970, where the biology professors had devised an experiment for measuring electrical resistance in plants, with very small microcurrents. Some interference was spoiling the experiment, they initially suspected the high-power Stanford Linear Accelerator atomic research machine, run by their colleagues, but found it was not so. Their only clue was it was likely man made, as it only happened on Mondays to Fridays. Eventually they traced it to the initial trial runs of the BART rapid transit, 1,000v DC with running rail earth return - the nearest point being about 5 miles away!