With the operation continuing throughout the night, about 170 evacuees have now arrived in the Senegalese capital, Dakar on board British military aircraft.
Several hundred United Nations peacekeepers, in the country to oversee disarmament in accordance with the peace accord, are still missing. The UN says they are being held by rebels of Mr Sankoh's Revolutionary United Front (RUF).
Troops dig in
About 700 British paratroopers arrived at Lungi Airport outside Freetown on Monday, securing the area and forming a bridgehead in Freetown.
Our correspondent in Freetown saw dozens of people, mainly women and children, climb onto giant RAF Chinook helicopters to be flown the short distance from Freetown to the airport.
(Click here to see a map of Freetown)
Tension is said to be running high but there is unmistakable relief on the faces of those who are leaving.
The UK is sending more troops and aircraft carriers to the West African region, to support the paratroopers.
Nigeria is said to be considering sending about 1,600 soldiers to back up government forces in addition to Nigeria's contribution to the UN force, and the United States has offered to fly Bangladeshi troops to Sierra Leone although it has repeated that it will not send its own soldiers.
Tense situation
But the Foreign Secretary made it clear that British troops had no long-term combat role in Sierra Leone.
A number of EU and Commonwealth nationals were also to be taken out of the country.
Killings
At least four people were reportedly killed and many more wounded after shots were fired at thousands of demonstrators who had gathered around Mr Sankoh's home in Freetown demanding peace.
Witnesses said UN guards fired shots into the air to disperse the crowd, after some individuals threw stones at the house.
But Mr Sankoh's supporters reportedly responded by shooting from behind the UN guards at the protesters, using automatic weapons and rocket-propelled grenades.
UN hostages
The UN is continuing to put diplomatic pressure on Mr Sankoh and the leaders of neighbouring states to secure the release of several hundred of its peacekeepers who it says are being detained by RUF rebels.
The World Food Programme has also suspended the delivery of relief aid to about 100,000 people in the districts of Bombali, Tonkolili and Kailahun.
"We had to curtail some of our most vital operations in those areas due to the high risk our staff are facing there," said WFP regional manager Paul Ares.
(click here to return)
The UK Foreign Office has issued a hot line number for worried relatives of British nationals: 0207 8391010
It is expected that this evacuation will continue for days to come.
Sierra Leone crisis
2 May: Four Kenyan peacekeepers killed, 92 UN staff captured by rebels
3 May: Rebel leader Foday Sankoh promises to release prisoners
4 May: Six UN staff freed, 208 Zambian peacekeepers detained
6 May: 226 more Zambian troops reported missing
6/7 May: Confusion over reported assault on Freetown
7 May: US and UK advise nationals to leave
7 May: Britain sends military taskforce
Mr Cook said the situation in Freetown had become tense and an estimated 500 British nationals had been advised to gather at the Mamy Yoko Hotel to be evacuated.
The demonstrators gathered around the house, which is guarded both by UN soldiers and RUF fighters, to condemn Mr Sankoh's and his rebels.
The UN announced that it was moving 266 civilian personnel out of Freetown, leaving just 55 essential staff.
Related to this story:
Sierra Leone: The role of UK forces
(09 May 00 | UK Politics)
Picture gallery: Bloodshed in Sierra Leone
(08 May 00 | Africa)
UK orders Sierra Leone evacuation
(08 May 00 | Africa)
Britain's ties with Sierra Leone
(08 May 00 | UK)
UK military team in Sierra Leone
(06 May 00 | UK)
Renewed bid to free UN troops
(04 May 00 | Africa)
Peace without justice in Sierra Leone
(10 Feb 00 | Africa)
Farewell to the general
(01 May 00 | From Our Own Correspondent)
United Nations: Desperately needing help
(09 May 00 | Africa)
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