A bit late in the discussion, but you do see this in Roman HF (especially Simon Scarrow), and I hate it. Not so much that its British, but that it sounds too modern. I prefer to research Roman swears and get a little creative (I have a book on Classical Latin profanities). Perhaps it is worth going back and looking at the language your characters should use. My WIP at the moment has a cast of mainly Jewish characters, and sometimes I have to stop myself from them blurting out, 'Jesus Christ' or 'Lord/God' in a swear which would be blasphemous to them.
I really found it hard to get into Scarrow for that very reason. It was jarring to have Romans calling each other mate and sunshine, and using other colloquialisms that reminded me of my north London raised boyfriend at the time
My rule of thumb is that most profanity and insults stem from the universals, so bodily functions, sex, animals etc. Or as my Greek drama professor once memorably said in a lecture on Aristophanes, anything related to pissing, shitting, fucking or farting
Targets for insults are also universal, like physical attributes, intelligence, parentage. These things vary surprisingly little from culture to culture, and across the centuries.
I have a character in my ancient Egyptian novel who is very coarse and foul mouthed, and I have so much fun with his dialogue. I think my favourite was when he called someone a 'goat-fucking aristo-cunt'
(And yes, the play on words there is heavily reliant on its translation into English, but I gave myself a pass on that coz it made me laugh)
btw, I think I have the same book on Roman profanity as you
Off topic, I once read a translation of the Iliad and the Odyssey that was modern, brisk, and unflinching - I particularly remember the passage where Polyphemus is blinded for it's brutality. But I can't remember the translator! Possibly Robert Fagles?
Don't like Fagles either. My favourite is the Martin Hammond, because it just translates the words in strong, clean prose that preserves an accurate sense of the meaning without trying to imitate the style or get fancy with language.