The gargantuan sum means each family in the UK now sends £450 a year to Brussels on average - up £350 from the £100 bill in 2008.
In just one year the UK's net contribution to the EU rocketed by £2.8 billion from £8.5 billion in 2012.
The soaring bill does not include the latest demand for an extra £1.7billion, which David Cameron has refused to pay by the December 1 deadline.
The shock findings, discovered in Office for National Statistics (ONS) figures published today, come less than 24 hours after Treasury analysis emerged suggesting the Government had expected Britain's Brussels contributions would be £8.6billion in 2013 - some £2.7billion less than the real cost.
Tory MPs immediately called for the Government to stop pouring billions more into the EU until it slashes the size of payments to farmers in France and other nations.
Backbencher Peter Bone said: "We should not pay the increase in our EU contributions which is going to be about £25 billion extra in this Parliament until they reform the Common Agricultural Policy, because that was the basis on which Blair gave up most of the rebate."
The increase in Britain's contributions is because Britain's economy has grown more quickly than other EU countries.
The net contributions include the UK's annual rebate, which increased from £3.1billion in 2012 to £3.7billion in 2013.
In 2008 the UK paid £2.7 billion to Brussels - rising to £3.8 billion in 2009, £7.2 billion in 2010, £7.5 billion in 2011, £8.5 billion in 2012 and £11.3 billion in 2013.
Matthew Elliott, chief executive of Business for Britain, which is campaigning for fundamental reform of the EU, said: "Despite David Cameron securing a historic EU budget cut, the cost of the EU to UK taxpayers continues to spiral out of control.
"We cannot continue to write bigger and bigger cheques to remain a member of an unreformed and uncompetitive European Union. Business is struggling under mounds of EU red tape and the UK economy is threatened by yet another potential eurozone recession.
"We must secure a new deal from Brussels and that will only be possible through a referendum."
In its report on the UK's balance of payments, the ONS said: "In 2013, the UK made a net contribution to the EU of £11.3 billion. This was an increase of £2.7 billion from the net contribution of £8.5 billion paid in 2012.
"The increase was mainly due to the £3 billion increase in the UK's total gross national income (GNI) contribution.
"The GNI contribution is calculated based on the UK's estimate of economic activity within a budget year relative to other EU countries and can increase and decrease from one year to the next.
"The UK, like other countries, receives a rebate on its contributions to the EU, and similarly to its GNI contribution, it can increase and decrease from one year to the next.
"In 2013, the rebate paid to the UK increased £0.6 billion to £3.7 billion, from £3.1 billion in 2012."
We should not pay the increase in our EU contributions which is going to be about £25?billion extra in this Parliament until they reform the Common Agricultural Policy, because that was the basis on which Blair gave up most of the rebate.
A major cause of the increase has been Tony Blair's decision to agree to a 7 per cut in the rebate during negotiations on the last seven-year budget deal. It cost Britain £7billion over seven years.
Margaret Thatcher famously secured the rebate in 1984 by banging the table and demanding "our own money back" during a summit with European leaders in Fontainebleau, in France.
Downing Street also blamed the decision by Mr Blair to give up part of Britain's rebate as part of reforms, including to the CAP.
The Prime Minister's official spokesman said: "The Prime Minister's views on the EU budget are well known. He is absolutely clear that we should be doing all we can to bring down EU spending and get control of the overall EU budget."
A Treasury aide blamed Labour's decision to give up part of the rebate for the increase in contributions.
"This figure isn't the full picture of the UK's net contributions as it doesn't include the 2013 rebate," he said.
"But despite that the major reason our contribution is rising is that the previous government gave away more than £7 billion when it gave up nearly half the rebate."