The crew of Royal Navy vessel HMS Bulwark have rescued more than 1,000 migrants in just one day in their largest operation to date.
In one operation at least 10 pregnant women were saved. The latest mission brings the total number of people rescued by the ship to 2,700.
Britain has vowed to fight European Commission plans that will force it to take a quota of refugees.
The proposals, to be unveiled in Brussels this week, are in response to the deadly people trafficking from Libya which has seen hundreds drown off the coast of Italy.
"Emergency mechanisms" could be invoked by the end of the month to ensure Britain and the other 27 EU member states make a "fair and balanced contribution" to taking in "persons in clear need of international protection", The Times (£) reported.
The paper claimed the longer-term plan would result in the UK dealing with at least twice the present 30,000 cases of people seeking asylum each year.
A "redistribution key" would impose a quota based on economic and social factors and previous rates of taking in asylum seekers, it said.
The Home Office has said the quotas are unacceptable to the UK.
Germany, which had more than 200,000 applicants last year, supports the changes.
Hundreds of migrants were rescued from the Mediterranean at the weekend - but their journey will not stop there, as they tell ITV News.
Britain's flagship HMS Bulwark has been involved in its "largest operation to date", plucking more than 1,000 migrants from makeshift boats
As HMS Bulwark continues to rescue migrants in the Mediterranean, David Cameron pledged that Britain would not shirk its responsibilities.