Head teacher in 'approximated social grade' would be B. As others have said, though, 'class' is multifactorial. You can have an aristocrat working as a museum or playgroup assistant, D or C2 jobs and crap pay, but they're still upper class and likely wealthy. Poor aristocrats are upper class unless actually destitute. Highly successful working class people can be in social grade A, multi-millionaires yet still working class.
Premier League footballers are C2 (skilled manual) by occupation and mostly working class by 'class', despite earning millions.
Welcome to Britain 😂 though other European countries are as bad - including Ireland!