Yes - I used to use them quite often as a way of having an extra hour or two to finish writing something of an evening before posting it off. (Though I rarely used other than the north-facing London terminal stations - I worked at Kings Cross, so KX, St P and Euston were all a few minutes on foot or on my pushbike.) I remember when the system changed and you no longer had to pay the extra 1p postage. (Or was it 1d, becoming half a p, before it was abolished?) When it became just the same as the ordinary postage rate, but you had extra time to post things, I'd use it not just for letters, but for distributing newsletters/newspapers I was involved in publishing "hot off the press", if I wanted to get odd copies out to people quickly, ahead of the normal distribution.
I think there were post boxes on some of the relevant stations, as well as on the side of the trains, so if you wanted to post something securely (ie bypassing the sorting system before the item left London), but you wanted to do so before the mail train arrived to load up, then that was an option. (Again, for the extra nominal amount, originally; those boxes mentioned the extra fee on them too.) When the mail train arrived, one of the staff would empty that station box and seal it until someone - no idea whose job it was - opened it again the next day.
As has been mentioned, making the most of the system required having an idea of which parts of the country were served by which mail train routes; but for me, that was just part of the "general knowledge" needed to live a communicative life!
One thing not mentioned by anyone here I think is that besides posting regular post, you could also send Registered Post [tracked, segregated handling, and insured (ie what was combined with Express to become what's now called Special Delivery)]; but in that case you had to hand it in to staff on the train, not use the box, and get your proof of posting and so on (as at a regular, ie stationary, Post Office). I only ever used that system a handful of times. Of course you could also hand in non-registered items direct to the staff rather than using the box; I'd often get greeted by one of the TPO staff standing in an open doorway, offering to take a letter from me, as I cycled up the platform to find the train's letter box - I guess it made sense for them to check that anyone posting something was doing so on the correct mail train for the destination of the letter. (I always was, of course...)
All in all, the ability to post direct onto the trains was a very civilised and useful adjunct to the existence of the TPOs,