I have a BA from a US college in Classics, and I'm currently studying at KCL for a MA in Classics.
I am considering doing a PhD back in the States, but I did not take the GRE. I still do not understand if it is necessary to take it (for instance, what is the sense of the math section for admission to a PhD in Classics..) after having an MA. Also, is it hard to get into American Phds having a UK Master?
I'm not sure how competitive Classics is, probably less so than the very popular disciplines, but I imagine the applicant pool is generally very high achieving. With Classics, multiple language fluency will likely be a big factor in admissions, especially at elite schools. I applied to a couple of Comp Lit programs, which I suspect is a similarly niche subject which may have similar applicant numbers: there you're looking at 60 to 200 applicants for between 3 and 8 places probably, so at some schools the odds aren't bad at all.
I don't think a UK Master's will make it difficult to get in...the only issue might be the lack of formal language exams and or training (if, indeed, it was not a part of your MA). I know plenty of people with UK Master's in U.S. PhD programs, myself included (though I'm British).