Since there aren't exactly a lot of gates on Earth, wouldn't SG-23 (in the actual SG verse) operate out of the SGC since that's where the only working gate on Earth is? That said, it wouldn't be too far fetched for them to have somewhere in the UK where they would (un)officially call home. To simplify logistics and to avoid drawing undue attention to themselves, I think that the most logical place would be an air base where large aircraft are based out of, one that sees regular air traffic to far away locales. Ideally, it would be one where it's not unusual to see personnel from different branches, what we in the US would call a joint forces base. Alternately, they would be headquartered near a major airport with regular service to the US and team members would fly out commercially in civilian clothes. But that would be less than ideal if SG-23 was covert as somebody might get curious as to why all of these muscular, military looking gentlemen are constantly flying out to the US and back, unless they're given false passports to travel on every time.