Staff at the British Embassy in Tripoli, which is closing today against a backdrop of fighting between rival militias, are among those expected to seek sanctuary in Malta following the so-called “assisted departure” operation.
The embassy is moving to neighbouring Tunisia for the time being.
The Foreign Office has previously urged British people to leave the country.
Yesterday, a Foreign Office spokesman said: “We are currently carrying out an assisted departure. The majority of those being evacuated are British.”
The Plymouth-based HMS Enterprise moored off the capital city of Tripoli and dispatched a smaller vessel to fetch the evacuees. Between 100 and 300 Britons are believed to be in Libya.
Many of the consular staff were evacuated last Monday, but the ambassador and core staff remained, although they will now also return to the UK.
Since the overthrow in 2011 of Colonel Muammar al-Gaddafi by rebels supported by British and French air strikes, Libya has descended into a state of lawlessness as rival militias struggle for power and wealth.
In the past few days, sporadic fighting between rival militias has spread northwards in the capital, including into the area where the British Embassy is situated. More than 200 people have been killed in Tripoli and the eastern city of Benghazi in the past two weeks.
Any Britons unable to take advantage of the opportunity to leave have been told they should find their way home on commercial flights, with limited departures from Misrata and Maitega airports.
Last Wednesday, British Airways suspended flights to and from Tripoli due to the security situation at the country’s main international airport.
HMS Enterprise’s commanding officer, Commander Mark Vartan, said: “This is a period of uncertainty for UK citizens based in Libya, but we have been proud to play our part in enabling their move to safety.
“My ship’s company have adapted to the challenge superbly, making as much space as possible and providing essential food, shelter and security for the journey.”
Defence Secretary Michael Fallon confirmed the Royal Navy operation had been launched following Foreign Office advice.
He said: “I thank the crew of HMS Enterprise for their support and professionalism in carrying out this important task.”
HMS Enterprise left the UK in June for an 18-month survey deployment, and it had been on operations in the Mediterranean.
Last night, it was reported that 108 people had registered to leave on board the ship.
They are not thought to be diplomats. Two Irish citizens and one German are believed to be among them. Passengers are being given supplies for the journey.
The ship’s departure for Malta is not considered a rescue mission as there are still commercial means to leave Libya.
British ambassador to Libya Michael Aron has described the situation as “very sad” and said staff would return “as soon as security allows”.
Most western countries have now withdrawn diplomats from Libya.