HMS Bulwark is leading Britain’s contribution to an operation European leaders hope will stem the loss of life of refugees fleeing the turmoil in Africa and the Middle East.
The 19,000-tonne assault ship had been in the Dardanelles for the Gallipoli centenary commemorations in Turkey.
A Ministry of Defence spokeswoman confirmed the vessel set sail yesterday.
Bulwark will be supported by two UK Border Force cutters and three Royal Navy Merlin helicopters with sophisticated radar designed to spot small surface vessels over long distances.
It will also provide a floating refuelling platform for the Merlins – expected to be based in either Malta or Sicily – enabling them to extend the range of their patrols.
The ship will work in tandem with the surveillance helicopters to provide day-and-night searches covering ranges of more than 100 miles.
Bulwark is expected to continue operations for around two months.
More than 1,700 people are estimated to have died attempting to cross the Mediterranean to Europe so far this year.
European leaders came under pressure to tackle the emergency after up to 800 people drowned off the coast of Libya last week.
Prime Minister David Cameron said yesterday that military action backed up by improved intelligence on people-smugglers is needed to help ease the Mediterranean migrant crisis.
Mr Cameron said there is not “one single answer” to solve the problem, with more needed on top of search-and-rescue operations.
He said the UK had stood by Libya since the military intervention in 2011, telling Sky News: “I would say to people, if you’re asking for a different approach, do you mean we should have put boots on the ground, troops in Libya after the end of the conflict?
“I think that would have made matters even worse rather than better but we need to keep going, to form that national unity government.”
On human traffickers, the Prime Minister was asked if he could see any form of military action involving British forces to disrupt the illegal activity.
He replied: “We discussed in Brussels at the meeting of the European Union potential action against these traffickers.
“Everything would have to be within international law; you would want to see good levels of co-operation.
“But if we can do things to break up the gangs, to get rid of the boats, to stop the criminals involved, it’s not just military action that’s being looked at but also criminal intelligence, the intelligence we have, what more can we do, how can we work with the neighbouring countries to stabilise them.
“The truth is there’s no one single answer.
“Search and rescue in the Mediterranean, which the British Royal Navy will be taking part in, is one part of it but if it was just that it wouldn’t work. You need more.”
The Bishop of Manchester said Britain has a “moral responsibility” to help refugees from conflicts in which it has participated. The Right Reverend David Walker also said migrants trying to cross the Mediterranean were victims, not criminals.
Hundreds more migrants were rescued from a vessel in the Mediterranean by the Italian navy on Saturday. The 274 migrants were rescued off the Libyan coast, the navy said.
Meanwhile, 334 migrants who were rescued on Friday were dropped off in the Sicilian port of Augusta.