a high first class?

Far as I know, your thesis is marked A, B, C with A meaning straight through to award without amendments, B - with minor amendments and C-more amendments that examiner may require to sight before passing thesis.

Again, far as I can tell, to get an A you need to be spot on with everything, from theory and data down to referencing and punctuation plus use of language.

PhDs are not given classes.
You either pass, pass with minor corrections, have to resubmit or get an Mphil.

In the UK there is no grading. But there are various ways that people in the field will judge your work - grading isn't necessary.

'In the UK there is no grading'

Indeed.. whether you pass with minor corrections or major corrections it makes no difference as your degree certificate will just have 'PhD' on it...

You either get the degree or you don't...