More than 110,000 people have arrived so far this year at a rate of over 2,000 a day.
That is nearly 10 times the 223 a day who reached Italy or Greece by sea in the first two months of last year.
The surge adds further momentum to the Daily Express campaign for Britain to leave the EU.
Experts warned last night that the number of arrivals this winter signals there will be an even bigger surge when the weather improves.
It is likely to mean the total number of migrants reaching Europe this year will far outstrip last year’s figure of 1.1 million.
The blame for the staggering increase has been laid at the feet of German chancellor Angela Merkel and her Swedish counterpart for their open-door policy.
The new data on arrivals – from the International Organisation for Migration – has heightened fears that the EU’s migrant crisis is spiralling out of control.
Alp Mehmet, of Migration Watch, said: “This massive increase is indicates the problem, rather than being solved, is becoming increasingly more difficult.
“It will continue to increase. What some see as a manageable problem is in reality far from it.
“Looking at this as an issue that can be solved after people have arrived is wrong. It has to be tackled at source. If it is a tenfold increase in the winter months – just wait until the summer.”
The figures come as Britain awaits a June 23 referendum on EU membership, with campaigners who want us leave arguing that it is the only way to reaffirm control of our borders.
Steven Woolfe, Ukip’s migration spokesman, said: “While David Cameron tours Britain like a victorious king, declaring how successful his EU reforms are, everyday realities make him look more like King Canute.
“The southern shores of Europe are awash with economic migrants from all over the world.
“Cameron’s reforms will never prevent illegal migrants who succeed in staying in the EU from attempting to get to Britain.”
Yesterday’s shock figures showed that more than 102,000 migrants, mainly Syrians, Afghans and Iraqis, reached Greece’s Aegean islands so far this year.
The figure dwarfs the 3,952 documented by Greek police in the whole of January and February 2015 – before Germany and Sweden opened their borders to Syrian refugees last summer.
And it is nearly triple the 34,000 who arrived in the whole of 2014.
Kelly Namia, of the International Organisation for Migration, said: “I am surprised by these numbers for this year. Approximately one million people have arrived in Greece since January last year. It is very difficult to manage the situation.
“What happens in the future depends a lot on border controls in other countries. But if things stay as they are, we will see more arrivals throughout the summer.”
Referring to Germany and Sweden’s calamitous refugee policy, Ms Namia added: “The numbers have risen because the incentives to come have changed.”
At least 413 people have died during sea crossings this year.
The migrant crisis is the biggest mass movement of people since the Second World War and it has caused the EU’s border-free Schengen Zone to unravel.
Passport controls and border fences have been thrown up across Europe in a bid to cope.
Many arrivals are genuine refugees fleeing Syria’s bloody civil war but huge numbers are also economic migrants trying to take advantage of the chaos.
Thousands have headed to Calais and Dunkirk hoping to reach the UK.
The think-tank Migration Watch warned recently that three million asylum seekers will arrive in Europe in the next two years.