I know all schools are different but it really hasn't been a problem at dd's. She has a small scholarship topped up with a bursary. Trips generally aren't any more expensive than the local state schools. And the majority don't go on the expensive ski trip type, so she doesn't stand out that way.
Uniform wasn't really much more expensive than local comp (which is ridiculously costly) and is far better quality, so I can honestly say it's better value for money.
However her school does offer additional funding if needed for uniform, or for trips such as mfl exchange in ks4, providing they agree you can't afford it and it would help educationally.
Socially it's not been a problem at all. Partly because dd knows dc in real poverty, partly because she's just not that way inclined, and partly because of the other pupils attitude.
She has friends who are from old school landed gentry backgrounds, the very wealthy, normal families making huge sacrifices and another big bursary dc from a much poorer home. Nobody seems to care about where we live or what I earn. The odd snob would be quickly ignored by the majority alike.
I do think it very much depends on the school though. Don't get me wrong, dd's is very impressive and well known, but it's also very academic. Parents just after boasting rights with dc who are just marking time till they come of age aren't the type of pupil it attracts.
The pupils know it's not the easiest school to get into, and achievement is very much the thing to aspire to, rather than wealth. The competition for a bursary & scholarship is much higher than for a full fee place, so having one is viewed as proof of intelligence, rather than proof you are poor. One of the reasons they prefer bursary kids don't advertise it early on is because other dc tend to have overly high expectations of genius ability across the board. Ditto scholarships.
Do look closely at the school though. Another a bit further away we viewed purely to get some perspective on dds was very different. I got the impression that their bursary pupils were nothing but future exam results and should be grateful to be there, it was very cold iyswim. Another perfectly nice school just wasn't as big, established or wealthy, so very few bursary dc, and lots of expensive extras. At either of those two her experience would have been very different.