The BBC could never be privatised. As with the railways, the only deal that would ever be politically acceptable would be one in which the profits of one or more supposedly private companies were guaranteed by public subsidies. That's not privatisation. Is it? The railways should never have been subjected to this, and nor should the BBC be.
Instead, elect the Trustees. In Scotland, Wales, Northern Ireland and each of the nine English regions (I know, I know - but what other unit could you reasonably suggest?), licence-payers should each vote for up to one candidate, with the top two elected to serve a four-year term. There would also be a Chairman, appointed by the Secretary of State with the approval of the House of Commons.
The Trustees would meet in public under any circumstance when a local council would do so. And the candidates would be sufficiently independent to qualify in principle for the Remuneration Panels of their local authorities.
I don't think there'd be too much F*** Off, I'm A Hairy Woman then, would there?
This pattern should also be applied, with everyone having a vote, to Ofcom, to the Press Complaints Commission, and to the Human Fertilisation and Embryology Authority, just for a start.