I studied abroad for a year in the UK in college with classics as one of my majors, and I spent most of last year at Oxford and Cambridge, so at this point I’ve had a fair amount of experience at multiple American and British universities. The difference between the systems is not great enough that you won’t be able to adjust between them pretty easily. Greek and Latin instruction is much the same anywhere. The methods of assessment are a bit different, as others have noted, but that is not a huge issue.
You’ve chosen a fantastic set of schools for classics, and you’d have zero problems getting into PhD programs if you do well at any of them. I would lean toward Exeter over Warwick and Oxford over Cambridge for classics, but YMMV.