Personally I'd choose an arbitrary point like the year 2000, and split the BBC into "heritage" (nationalized body that holds all the archives, like the British

Personally I'd choose an arbitrary point like the year 2000, and split the BBC into "heritage" (nationalized body that holds all the archives, like the British Library or the British Museum), BBC Radio (taxpayer funded by DCMS, this is not very expensive) and "continuity TV" (commercial body that has to fund itself like any other). This does mean Doctor Who getting split in half, but that's not the worst that's happened to him/her.