At the Port of Dover in Kent, officials said this morning that cross-Channel ferry operations were operating "as far as possible".
Passengers are being advised to allow extra time for journeys ahead of possible road blockages on the A2 and A20.
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Professor Sir Brian Jarman told BBC Radio 4's Today programme "it's likely" that similar events to Gosport have occurred in other hospitals.
Tory Eurosceptic Jacob Rees-Mogg played down the significance of the deal struck by the Government to win over pro-EU rebels.
The Tanaiste issued the warning to the UK ahead of a visit to Dublin by European Commission President Jean-Claude Juncker.