That's interesting.
I was at Cambridge in the early 90s, so only a few years earlier than you. My college was roughly 50/50 state/private but there were some colleges at that time with much higher proportions of privately educated students and others with higher proportions of state. Around 80% of the students at my college on my particular course were privately educated, so I did feel rather outnumbered!
I always knew exactly which of my peers were privately educated and which were not, and I definitely felt that there were real differences - mostly in terms of attitudes and mannerisms rather than anything substantial, but it was very evident. There was definitely a sense of solidarity amongst the state educated students, as I think many of us found the public school vibe pretty off-putting at first. We learned to look past it as we got to know people better, of course.
I don't think it was a frequent topic of conversation after the first term or so, but the schools people went to came up a lot in freshers' week - tons of people asking each other which school they went to etc. I found it utterly bizarre because obviously, nobody would have heard of my state comp and I didn't really care which school anyone else had been to!
But it clearly mattered quite a lot to those who had been to the "big name" public schools. Probably not so much to the kids who went to the small local indies, but they were a bit invisible at the time!
I had gone to an excellent comprehensive school, and had been far more successful academically than the girl I l had lived with during my gap year, despite her having gone to a "big name" school, so it didn't ever occur to me to feel hard done by. However, socially, it was certainly a factor. In that first year in particular, a lot of the privately educated students seemed very alien and different to me. The way they presented themselves was not in line with what I was used to, and I interpreted it at first as them being rather full of themselves. I subsequently realised that that wasn't actually the case, it was just their normal way of talking, and they had no intention of coming across that way. Once I had learnt to look beyond the veneer, some of those privately educated students actually became very good friends, but I wouldn't have imagined that possible at first!!