A Royal Navy destroyer is on its way to Cyprus, carrying the first Britons to be evacuated from Lebanon by sea.
Children were among those boarding HMS Gloucester
HMS Gloucester is carrying 180 of the most needy cases, including children. Up to 5,000 more Britons are expected to follow over the next few days.
Israeli forces temporarily lifted their blockade of Beirut's port - in place amid the worsening Middle East crisis - to allow the vessel to leave.
HMS Gloucester is expected in Cyprus in the early hours of Wednesday.
Its captain, Commander Mike Paterson, said there would be beds on board for all 180 Britons.
"They should be able to get fed and have a rest. By the time they get up in the morning, we should be in Cyprus," he added.
Britain began its major evacuation as Israeli forces and Hezbollah fighters continued to carry out cross-border attacks.
Israel launched an air offensive on targets in Lebanon last week following the capture of two of its soldiers by Lebanese guerrillas. Hezbollah fighters have been firing hundreds of missiles into northern Israel.
About 230 Lebanese people and 25 Israelis have been killed since the fighting began.
One of the British nationals evacuated on Tuesday was mother-of-two Samantha Bradley, from the West Midlands, who described the ordeal of the past few days.
"They were bombing quite near to our house so we moved away. We moved up into the hills and last night they bombed... the village where we were staying."
The family had earlier escaped injury when a bomb blast smashed the back window of their car as they fled Beirut.
The evacuees are due in Cyprus early on Wednesday
Another evacuee expressed anger at what she deemed a lack of international action to end the violence.
"It's really hell. I don't know what the world is doing, just watching innocent people being killed every single day," she said.
Most Britons are expected to be evacuated by sea, but Wing Commander Carl Scott, chief of staff of Joint Helicopter Command, said five Chinooks were currently providing support to British officials in Beirut.
He said: "We flew in [EU foreign policy chief] Javier Solana and took the opportunity to take 40 people out - the ill, the young, elderly and those you would expect to need to be taken out."
Wing Commander Scott added people were being taken to a reception area at RAF Akrotiri, in Cyprus.
So far, 5,000 people out of about 22,000 in Lebanon who are eligible for evacuation by the UK have requested to leave.
BBC correspondent Clive Myrie said Tuesday's evacuation was being seen as a "dry run" for a mass evacuation later in the week.
British Ambassador to Lebanon James Watt said: "We are going for far bigger numbers [on Wednesday]."
Officials were expecting to move between 3,000 and 4,000 Britons - although some did not want to move straight away, while others were trapped in the south of the country.
"They are the ones we are really concerned for," he said.
Earlier on Tuesday, Prime Minister Tony Blair denied the UK had been tardy in moving its nationals from Lebanon.
UK FOREIGN OFFICE ADVICE
Advice to British nationals in Lebanon is to stay put but be ready to move at any time
British and dual nationality citizens should call the Foreign Office on 0207 008 1500or the embassy in Beirut on (00) (961) (1) 990400
Six Royal Navy ships in the region for rescue operation
Britons in Israel should avoid all but essential travel areas within 25km of northern border
"We are doing absolutely everything we can to make sure everything happens as swiftly and properly as possible," he told reporters.
A rapid deployment team in Beirut and reinforcements in Cyprus had been deployed to help with the "big logistical operation", he added.
A Foreign Office spokesman said embassy staff were working "flat out, 24 hours a day" in "very difficult and trying circumstances" to do everything possible to help British citizens.
As well as HMS Gloucester, HMS York, HMS St Albans, HMS Illustrious, HMS Bulwark and the Royal Fleet Auxiliary Fort Victoria are now in the region after being sent from other parts of the Mediterranean.
Meanwhile, six military Sea King helicopters left the Royal Navy base at Yeovilton, Somerset, shortly after 1500 BST for Cyprus to help with the evacuation.
The British High Commissioner to Cyprus, Peter Millett, said Cyprus would be used as a "transit point" for people leaving Lebanon and wanting to get "home to their loved ones, as fast as possible".
Are you a British citizen living in the region or do you know of anyone directly affected? Send us your stories or e-mail your pictures using the form below. Please include contact telephone number if you are willing to talk to us further.
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.