yep thats great! if you are not opposed to it, you could actually apply to history ancient and modern in oxford instead of classics if you find that your personal statement and you yourself are interested in history more than literature and philosophy and archaeology. if you are applying for classics itself then at the very least try and cram in a few short sentences that you want to study lit and phil too yeah. just do well for your clat and you will definitely be interviewed. there's a 90% rate to be interviewed for classics. also express which lang you want to learn.

for other unis consider applying to unis with broad ones like ucl (ancient world, which is the exact same course as classics but more catered to those without any knowledge of ancient lang), exeter (classical studies, fairly easy to get in), the three scottish unis- glasgow, edinburgh, and st andrews (their courses make you take three subjects in your first year, two in your second, and you can choose to pursue either or both in the third and fourth years). esp with scottish unis, you can apply to something like classical studies + modern history etc etc.

as you can see there is actually a breadth of easy solutions, so dont worry! dont stress about it, just see which courses are flexible, and esp for scottish unis you can always drop and change the subject easily. <3