It’s already happened
James Meek: The NHS Goes Private, 22 September 2011
“... the views of the medical profession. It didn’t work. Tony Blair’s first health minister, Frank Dobson, read its funeral rites when Labour came to power seven years later. Yet at the turn of the millennium, Alan Milburn replaced Dobson and Labour introduced a new, more radical version of that market. It was Labour that introduced foundation ... ”