you have a chance.
if you're studying classics (and not classical studies) you will learn latin and greek at some point. where there is no requirement of prior knowledge of these languages, people may look for evidence of linguistic ability, e.g. a good grade in a modern language at gcse.
however, an interest in classics is the main thing that's sought for. if you have time in between studying for your a-levels, take advantage of your own enthusiasm and don't hesitate to explore the classical world! one way is to do this by lots of reading, or listening to podcasts and watching videos alongside other forms of media. alongside this, you can go to museums with exhibitions of ancient artefacts, or to archaelogical digs. there are even classics lectures available to the public in some areas - look out for advertisements and events pages, and there'll be something in due time

besides, you have humanities on your side! skill in essay-writing and critical analysis, especially of sources, is highly valued in students of classics. english lit and history may also have helped you build a sustained judgement around your opinions, and that is also a good part of rhetoric to have.
classics and english together would give you the opportunity to study classical literature along with english literature. the course also places emphasis on reception of classics and classical drama, so if there are several aspects of classics that interest you, and you want to learn about them in depth along with english, this would be a course to consider.
note that to take classics and english course at oxford, you'd need to take two admissions tests. here's the page for more information:
https://www.ox.ac.uk/admissions/undergraduate/courses-listing/classics-and-english?wssl=1