It is a rise of £13 million on 2014 and the second highest total for the past 10 years.
The Leave campaign attracted criticism for using a slogan that said: “We send the EU £350 million a week”.
Remain campaigners said the figure was misleading as it did not take into account the money the UK receives from the EU in the form of a rebate, as well as payments made to the public sector.
The new data appears in the latest breakdown of the UK’s current account, known as the Pink Book, published by Office for National Statistics.
The figures suggest the UK’s gross contribution to the EU last year, before the application of the rebate, totalled £19.6 billion - about £376 million a week.
But the Treasury pays the UK’s contributions to the EU after deducting the value of the rebate. The rebate in 2015 was £4.9 billion. Subtracting this from the gross contribution gives a figure of £14.7 billion.