A Royal Navy warship set sail from Beirut last night with about 180 Britons fleeing Lebanon aboard.
HMS Gloucester, a Type 42 destroyer, was heading to Cyprus where it was expected to arrive in the early hours of today.
With two larger vessels on their way, Downing Street signalled that the departures would accelerate in the coming days.
"You will see tomorrow, as facilities arrive, the pace of that being stepped up considerably," Tony Blair's official spokesman said.
"I think people will see a step change in that in the next 24 hours."
In the Commons, the Prime Minister told MPs that 5,000 of the estimated 22,000 British nationals and dual nationals currently in Lebanon could be out of the country by the end of the week.
"We are working as hard and as quickly as we can to ensure that we are able to evacuate all those who wish to leave," he said.
The aircraft carrier HMS Illustrious and the commando assault ship HMS Bulwark - both bigger than HMS Gloucester - are heading for Beirut for the next round of evacuations.
In Beirut, other western nations - including the United States, Canada, France and Italy - were evacuating hundreds of their citizens on warships, chartered ferries and helicopters.
The departures came as another barrage of Hezbollah rocket fire left one dead in the northern Israeli town of Nahariya, while Israeli air raids continued across southern Lebanon.
More than 230 people have now died in Lebanon in seven days of fighting.
The Captain of HMS Illustrious, Commodore Bob Cool-ing, said the six Royal Navy vessels now in the area could evacuate up to 10,000 people between them.
"Clearly we have not done it on anything like this scale before, but we know what's required and we have done a lot of training," he said.
In the Commons, Mr Blair urged Israel to show a "proportionate" military response.
But he also made clear that he held the militant groups Hezbollah and Hamas responsible for the current crisis.
He said the kidnapping of three Israeli soldiers in Gaza and on the Lebanese border had been deliberately designed to provoke a backlash by the Israelis.
And he also hit out at Hezbollah's backers in Syria and Iran - directly linking Tehran's support of the militant group to roadside bomb attacks on British troops in Iraq.
"Hezbollah is supported by Iran and Syria, by the former in weapons, weapons incidentally very similar if not identical to those used against British troops in Basra; by the latter, in many different ways, and by both financially," he said.
Mr Blair, however, appealed to Syria to intervene with Hezbollah to end the violence.
Mr Blair said it was now essential for the international community to take action to "stabilise" the situation in both Lebanon and Gaza.
Pope Benedict XVI last night lent his support to the G8 summit declaration on the Middle East, which blamed the militant groups Hamas and Hezbollah for the escalation in fighting and which urged Israel to exercise restraint.
"I fully agree with the G8 communique," the Pope said when he returned to his Alpine holiday retreat after an excursion in the mountains.
The Iranian parliament's speaker yesterday warned that no part of Israel was safe from Hezbollah attacks and heaped praise on the Islamic militants in comments that challenged his government's declaration of noninvolvement in the Middle East fighting.
The speaker, Gholam Ali Haddad Adel, sounded as though he was speaking on Hezbollah's behalf at an anti-Israeli rally of more than 5,000 people.
Addressing Israelis, Haddad Adel said: "The towns you have built in northern Palestine (Israel) are within the range of the brave Lebanese children. No part of Israel will be safe.