The question is not whether the government can tell the BBC who to have on the panel of Question Time, but whether the BBC can tell the government to make a minister available to the programme.
The answer most clearly is no, it is up to the government to decide if they want to be formally represented on a programme aimed more at producing what some people see as ‘good tv’ rather than a discussion of the latest political developments.
Personally I feel that watching that poor sad angry man, Alastair Campbell, declining slowly into the status of embarrassing uncle with his stories of When I was in Patagonia or of How I used to be a contender is more like a freakshow than a programme worthy of the political wing of the BBC.