I don't know that you'll find a semi-private tour offering that combination. The two museums are about 0.8 miles apart (per Google maps), and the British Museum in particular can have a considerable line-up of people at the security check-point. Even if a tour hit the British Museum first, there would still be a lot of time in transit for which you'd be paying the guide but not receiving in-museum guide services. Those museum buildings are large, so just walking from the door to the point where the tour begins and from the end-point back to the door can take many, many minutes.
Have you considered joining separate tours offered by the museums themselves?
British Museum one-hour focused morning tours; these tours begin at 9 AM, an hour before the museum opens to the public. That could be heaven.
Other British Museum tours, at least some of which are free.
Free daily tour at National Gallery, 2PM - 3 PM
In addition, both of the museums have audio guides that provide explanations of some of the objects on display. I don't remember their cost, but it is typically modest.
I imagine you could arrange a private tour of any combination of sights you like, but I think the universe of people qualified to guide you through both an art museum and an ethnographic/history museum is not large.