There used to be some District services which ran through to Southend
(between 1910 and 1939). I have no idea what colour the trains were,
though, and they would have been steam-hauled surface stock rather
than electric "tube" trains.

More precisely, they were hauled by electric locomotives from
Ealing Broadway to Barking, then by steam to Southend. The District
conveniently had some locomotives that they'd bought for the Outer
Circle service (see under http://www.davros.org/rail/culg/circle.html),
so they were now available for the Southend trains.

The LT&SR supplied the rolling stock (new trains from 1912, with
retention toilets), so it presumably would've been in their livery.

[Sources: London's Underground, 7th edition; The Age of the Electric Train]
--
Mark Brader | "[Your orders are] to figure out what I would have ordered
| you to do, if I really understood the situation ... [and]
Toronto | to follow those orders I hypothetically would have given."
-- Shan (John Barnes, "Earth Made of Glass")