It's true: we really do have a weird hang-up with social class. It's when you've lived abroad for any duration and then returned that you really do notice it, but it's a 'thing' and it's pretty evident to anyone. It also make things (and people) depressingly, boringly conformist.
Cost of living isn't great.
Complaining is something that's pretty much endemic in any society, but we seem to get a bad rap for it. We are, however, a fairly reserved (some might say insular) society. I find that very noticeable whenever I've been away in the States or on the continent. When I come home it seems that people are more morose and less outgoing than they are in those places.
Being monolingual is a disadvantage. I'd love to be fluent in another language. The issue is if you don't use it constantly, you lose it.
Teachers, professors, doctors etc are treated with a great deal of respect in other countries: Norway and Germany just for two. Here, those people seem to be roundly despised (public sector workers?)
Racism is a problem in many countries. The good thing about Britain is that at least here it's viewed as being beyond the pale, whereas elsewhere it can be so casual and commonplace it's pretty much accepted.
The volume of traffic on our roads is horrendous. Likewise our very overpriced rail network runs to capacity even on an average day.
An outdated constitution, hereditary head of state and upper house, together with a very nepotistic old boys' network, are vastly at odds with a modern-day, democratic, meritocratic society. Our system is long overdue an overhaul.
Negatives aside we have a country with one of the richest cultural histories on the globe, diverse wildlife, miles upon miles of beautiful coastline, beautiful historic cities, wonderful humour, and an attitude of championing the underdog. I sometimes wish we had a better sense of community and/or had come further toward social and sexual equality. Nowhere is perfect.