What house you live in doesn't really determine what class you are. It's more about what you can afford.
In this area, if I had to label it, I would say it is middle to upper middle class house. It's in a nice area. For comparison, I have a professional job and am from working class parents. I live in a 4 bed £450K house which is a bit less fancy in a slightly cheaper area. I can just about afford it as a single person in my 50s as I got on the property ladder in my 20's so have equity, and I inherited some money from my parents.
I am probably middle class although I think it covers a wide range. My goal is to downsize and pay off my mortgage in the next 10 years. I don't think my class will change if I move to a cheaper 3 bed.
Had I stayed married and my husband earned the same as me we would be able to afford that house, although as ours is plenty big enough and still in a nice area, we would probably stay put, spend money on this one, over pay on the mortgage and pensions, travel more and have more pets. I would pay someone to clean and decorate.
As another poster said, the people who know you won't think any different regardless of your house choice and those you don't know, don't matter.