This was reported in the press back in January

"The Dover Harbour Board, the body that oversees the operation of the largest British port still in the public sector, has applied to the Transport Secretary for voluntary privatisation. A sale, according to insiders, could net as much as £350 million for the Treasury, which has earmarked £16 billion of publicly owned assets, including the Post Office, for injections of private capital"
The Times January 27, 2010

With typical reaction the Mail reported the same story on the 8th Feb with the headline
"White Cliffs of Dover to be sold to the French to help reduce Government's debt"

In fact, the government is expected to make a decision on privatisation of the port this autumn as a second public consultation on the scheme ended last week
I think the cliffs still belong to the 'bluebirds' but we are talking the Mail here!

Dover is Europe's busiest ferry port (published accounts at the port from 2008 revealed that it made nearly £25 million in profits on revenues of around £61 million)

In January 2010 the Dover Harbour Board submitted a proposal under the Ports Act 1991 to government "leading to the voluntary privatisation of the Port of Dover." by means of a formal application for an injection of private capital.

Other major ports were sold off under the 1991 Ports Act, but Dover was retained because of uncertainty over how construction of the Channel Tunnel might affect it.

The port has operated as a trust for 400 years and with no shareholders all revenue goes back into the business.

The Unite union has said that privatising Dover would be against the national interest; their .national officer for docks and ferries Julia Long said: "We need a first-class sea port like Dover to be in public hands.
"There is simply too much at stake to leave the running of this vital link to Europe in the hands of those who will milk this national treasure for profits at the expense of the travelling public and British commerce."
However the Port of Dover board argues it would be for the long-term benefit of UK transport
"As a trust port, the Port of Dover is unable to finance significant additional capacity when required as its status as a public corporation does not allow it to borrow,"

Dame Vera Lynn is reported as saying she would support a scheme for local people to buy the port of Dover, if the government decides it should be privatised.

BUT - As Bob Crow, the General Secretary of the National Union of Rail, Maritime and Transport Workers (RMT), points out -

"The Port of Dover is already owned by the British people as a national asset. Why would you want to buy something you already own?"