The surprise demand was branded “outrageous” by Eurosceptics in Mr Cameron’s own Conservative Party, and will heap additional pressure on the Prime Minister as he fights to defend the seat of Rochester and Strood from Ukip in a crunch by-election.
The Prime Minister last night held talks at the European Council summit in Brussels with Dutch counterpart Mark Rutte, who is facing a similar surcharge, on how they can challenge the demand for cash.
Mr Cameron made no comment to waiting reporters as he arrived for the second day of the summit this morning.
The surcharge - which would add almost a fifth to the UK’s annual contribution of £8.6 billion - is intended to reflect Britain’s better-than-expected economic performance relative to other EU states.
It results from an EU recalculation of national incomes dating back to 1995 and taking into account recent changes in the rules to include economic activities such as prostitution and illegal drugs.
Preliminary figures seen by the Financial Times suggest that Britain is facing by far the biggest top-up, while the Netherlands is being asked for an extra 642 million euro (£506 million).
By contrast, Germany receives a rebate of 779 million euro (£614 million), France 1 billion (£788.7 million) and Poland 316 million (£249 million).
Conservative former Cabinet minister John Redwood said Mr Cameron should refuse to pay - and should amend the law if necessary to make clear the UK regards the demand as “illegal and unacceptable”.
Mr Redwood told the BBC Radio 4’ Today programme: “This is a very large increase in tax on the British people, imposed retrospectively without their permission.
“It offends all our principles of natural justice and fair taxation. The British people are already paying too much tax and he last thing they intend to do is sent another £1.7 billion to the Commission so that they can behave in the way they just have overnight.”
Ukip MEP Patrick O’Flynn said: “The EU’s budget surcharge is effectively asking UK taxpayers to fork out for the disaster of the eurozone. Totally outrageous.”
Conservative MP Mark Pritchard said: “The timing and content of the EU budget demand shows how inept Brussels is. Brussels needs to work with the UK Government, not work against it.
“Unless this behaviour changes, the EU referendum could be brought forward. Europe should not penalise the UK’s economic success whilst rewarding France’s economic failure.”
The surcharge is due for payment on December 1 - just days after the Rochester and Strood vote on November 20.
A Downing Street source made clear that the UK will challenge the demand.
“It’s not acceptable to just change the fees for previous years and demand them back at a moment’s notice,” said the source.
“The European Commission was not expecting this money and does not need this money and we will work with other countries similarly affected to do all we can to challenge this.”
Mr Rutte described the demand for more cash as “an unpleasant surprise (which) raises an awful lot of questions” and said his government will “look at all aspects, including legal ones”.
Commission spokesman Patrizio Fiorilli said the figures were produced by a “mechanical” calculation and the demand was “not politically motivated”.
“Britain’s contribution reflects an increase in wealth, just as in Britain you pay more to the Inland Revenue if your earnings go up,” he said.
The Commission’s demand for additional funding from Britain was strongly criticised by the leader of the Conservative MEPs, Syed Kamall.
“The European Commission is penalising Britain for taking tough decisions, putting in place a long-term economic plan and for having the most successful economy in the EU while actually rewarding France for being an economic basket case,” he said.
“David Cameron is absolutely right to stand up to this attempted daylight robbery by the EU.
“This is outrageous and harms the EU’s relationship with Britain. At times like this, the European Commission can be its own worst enemy.”
Conservative MP Peter Bone said: “We are just being taken for a ride. We are paying more and more in and getting nothing in return.
“Roll on the referendum - this will just strengthen the resolve of the British public to get out of this superstate.
“They are trying to rub David Cameron’s nose in the dirt for for having the audacity to stand up and say freedom of movement is wrong.”
The row over the top-up payments overshadowed other events at the summit, where leaders agreed a deal in the early hours on an EU-wide 40% target for greenhouse gas reductions by 2030.
Mr Cameron also announced an additional £80 million of UK aid for Ebola-hit countries in West Africa, as he tried to shame fellow EU leaders into giving more.