Sadly class and financial status are two different things. And this is a question that has been raising its head for centuries in this country.
As has already been stated, traditionally social class is pretty outdated now, because sadly, in many areas education does not count for what it once was and no longer guarantees a good wage.
Many trades people will earn more than you, and that's because its more physically demanding and you have a limited shelf life. However, some of that money has to go on private pensions.
You on the other hand are a teacher and a government worker. I just left the private sector not so long ago for less money...yes that sound weird but in the Civil Service I get a massive pension contribution which makes up the difference. Like you, I am speculating to accumulate. A lot of working class people are on the breadline and will be so right into and including their retirement. Its unlikely you or I will be in this position.
I started life as working class, based on the education of my parents. But Dad got a really good wage, a really nice house and we even had a pony. Mum and Dad split up and we ended up on a council estate...and I flourished. All three of us kids got degrees, two of us own our homes outright and all have above average income. My husband is a professional (also from a Council Estate) and I am a Senior Manager in the Civil Service and we are both in a Union. So what social class are we now? I identify as working class, because that is who I feel I am. Technically, we are both middle class, based on our education, property, lifestyle and professions.
But I am not rich or even well off. We have three kids who are never going to get on the housing ladder, rental is extortionate and quite frankly we could retire if we didn't want to try help them. And that's the other thing, we have a house that is paid for and we know that one or both of us will end up in care and the kids are unlikely to get anything and that/s why we need to help now. I could actually do with retiring early due to my caring responsibilities but if I do, I won't be able to afford the travelling I need to do for my caring responsibilities or help the kids.