Orange stated an intention to cover tunnels on most (mainline) railway routes as far back as 2003/4. The idea was to simply erect sites near to the tunnels, rather than any clever system (e.g. leaky feeder) inside.
I wrote a story on this for a trade paper, but sadly it never went online so I can't refer back to it for the finer details. The ECML was, as you'd expect, one of the lines mentioned.
I have to assume that it did so wherever it could*, but possibly had issues with planning at some places and that's why. And, it would have only been one network at the time (albeit now part of EE so benefiting Three, Virgin, T-Mobile users etc).
* There's a cell site just by the tunnels near Hadley Wood, but I don't know if it's Orange/EE. What's more, you generally lose signal in the long tunnel there - or at least going one way. You can, however, see how Network Rail has put antennas up to cover them for GSM-R - actually at the tunnel mouths!