What is really interesting is to watch the RTT while you run a speed test.
Other trains don't seem nearly as bad. I'm not sure how much of that is due to different construction or (in the case of other modern(ish) rolling stock) anything like the repeaters you mention (though as all the franchise owners are cheap-arses I very much doubt that tech has been paid for by any of them!).
There are a number of places where trains skip around at a goodly speed in what is probably a packed area by way of phone cells, so there will sometimes be a significant number of cell-to-cell hand-offs. Having said that, as I grew up (well, more-or-less) before mobile phones were common I'm still slightly impressed that the whole cell hand-over thing works at all mid-call at 80+mph so maybe they are not much of an issue unless the destination cell is already saturated at the time.