If you meet their requirements then you should get an offer. You offer MAY be slightly lower than for a UK student… but for this level of unis I doubt it. Especially not Oxford or Cambridge.
Kings tells you on their website for Classics (Greek and Latin) BA:-
Required subjects:
Latin or Ancient Greek
Preferred subjects:
Classical Civilisation, Ancient History or History preferred.
Go look up each page. Doing your own research is a key skill needed to do well at a British uni as no one holds your hand
You can apply to only one of Oxford or Cambridge.