The Royal Navy vessel HMS Gloucester has started rescuing Britons from Beirut. (Picture: Royal Navy)
The first two-hundred-and-fifty people are getting on board, and will be taken to Cyprus.
Royal Navy warships are standing by to help up to 12,000 Britons and 10,000 dual nationals get out.
Some of the first people to flee the Israeli air strikes have already arrived in Cyprus.
The group of around 60 elderly and sick Britons were airlifted from the capital Beirut in the three UK helicopters that took EU foreign policy chief Javier Solana for talks with Lebanese Prime Minister Fuad Sinoria.
Another 19 Britons were also later airlifted from Beirut to Cyprus.
Tony Blair insisted Britain was acting "as quickly as we possibly can" to get the Britons to safety.
Mr Blair said: "We have acted as quickly as we possibly can. We have taken out of Lebanon the first 60 people - that was done yesterday.
"The first ship will come today, so obviously we can take far greater numbers out."
Mr Blair said British nationals were likely to be taken to Cyprus once they were evacuated from Lebanon.
He added: "We will do everything we can to get people out as quickly as possible."
Foreign Office Minister Kim Howells said the "safest and most practical" option for removing the bulk of those trapped in the country was by sea.
Royal Navy destroyer York is waiting offshore to take part in any evacuation and the aircraft carrier Illustrious and assault ship Bulwark are approaching the area.
A "rapid deployment team" from the Foreign Office has arrived in Beirut to assist embassy staff and, together with a military reconnaissance team, will carry out "detailed planning for a possible evacuation".
Mr Howells said: "For the moment we are advising British nationals in Lebanon to stay put, exercise caution, keep in touch with the British Embassy and heed local advice."
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