I have a bit of knowledge (second hand) of a student in an accredited IB programme in a private (RC) girls' high school in IL to a private girls' secondary in SW London that is something of an international school. The move was very smooth on all fronts. She started the IB programme in her first year of high school and transferred to London after two years.
My own DCs went through RC elementary and public high school in the US, both well regarded schools. I echo Sheherazade's assessment of the strengths of American schools. An American student who goes all the way through to HS graduation taking honours classes and pretty much all APs for the final two years is imo a superior student to a British one, and not only because of the breadth of courses required (math, science, English, humanities, language, electives) but because of the depth at which the really good students work (those who get a 4 or 5 in AP courses).
My oldest three DCs were all accepted into highly selective US universities. They did almost all AP courses for their final two years of HS and found themselves very well prepared for third level courses. Foreign language was the only course they didn't do at AP level because they all dropped Spanish and took another language instead, starting from scratch. Honours level proved enough for them to pass their university language requirements easily.
If your local public schools are well regarded, then they will stack up well against anyone else in the world. I would be leery of an IB programme that is not yet accredited. Middle school is only three years after all. Or at least it is around here. I would prefer to join a programme that was already tried and tested.
Every year a few students from the RC elementary who lived in the nearby very large city applied for admission to the extremely selective city college prep public high schools and they all got in. The RC school was very strong in all areas except math, but those students wishing to overcome that enough to pass the city selection exam went to summer school between 7th and 8th grade in a local RC high school. DD3 also had to endure the dreadful math teacher in the RC elementary, but was able to go to summer school in our local public high school in the summer before her freshman year and the next summer too so she is now on track for (AP) BC Calc in her final year like the rest of the DCs. My advice is not to overlook summer school as it can give a huge boost if there are areas where a DC is struggling or is badly taught. And don't overlook RC high schools' summer school offerings.
The reason I focused so much on DD3's math is that our HS places students in science levels based on where they are in math. Students not taking honours math did not get to take honours science courses.
I know two families who moved house specifically to get into a really good middle school (its top maths grads tend to start high school at pre calc and just take various AP math courses every year for the next three years to while away the time) -- so another nugget of advice
would be 'where are the local Russian families sending their children?'