I doubt that Army or the RN would want to take over the RAF's responsibilities, but their is a strong case for some streamlining and managerial cost cutting.
1. The AAC could take over the RAF's rotary winged operations. They do service the army afterall.
2. JFH should operate under Naval Command. As the Tonkas are retired what will be JFL could be expanded still further into a much more flexible and more capable unit for maritime or land deployment.
3. I see a very strong case for selling off as many Typhoons as possible other than those needed for AD. The F35 can do everything else better.