Well I'm reassured on reading this thread, that I'm not the only person with problems at LHR e-gates. Those last two words were deliberately chosen. I have no problem with e-gates anywhere else. I renewed my UK passport about a year ago and it has never worked at LHR. Neither has my wife's, whose passport was renewed at the same time. It isn't a chip problem as the passport works perfectly well anywhere else and I can read the chip on my phone. My previous passport worked perfectly well, so the idea that I share a name and DoB with someone undesirable doesn't really make sense, nor the fact that my wife also gets flagged.
My 2 cents is that LHR bought a batch of defective readers on the cheap and they only work half the time, a bit like BA's IT.