Not there's anything wrong with modelling an interstellar Empire on the British Empire, but there are plenty of alternatives for modern space opera fans:
David Drake's RCN series is an excellent fit for fans of the Honorverse and the first volume, WITH THE LIGHTNINGS is in the BAEN FREE LIBRARY. No need to worry about a british-style regime, as the Cinnabar empire is modelled mostly on Republican Rome. Any Space Opera series with a librarian as a protagonist is worth looking into.
John Ringo's LOOKING GLASS WAR/VORPAL BLADE series is also very good adventure SF. Just bear in mind that the overall narrative and individual volumes vary from light and playful (volume 1, INTO THE LOOKING GLASS verges on farce at times) to seriously realistic (volume 2, VORPAL BLADE, for example). No british-isms either, as the protagonists are US Space Marines. And a "housecat" named tiny.
Recommended. (Actually, I'm minded to go reread the series.)
Weber himself has another, shorter, space opera series collected in EMPIRE FROM THE ASHES with minimal brit flavor that is also a lot of fun. (Though the female lead does sport an Elizabethan back-story.)
As for the Honorverse series, the reason the primary good guys are modelled on the British Empire is because Weber had the Napoleonic Wars in mind when he started the series. Hence their antagonists are suspiciously french-like. As the series has evolved he has modeled the different star nations after regimes/cultures from other eras and regions, so the Graysons are vaguely 19th century mormonic and the Solarian League maps most closely to the contemporary European Union.