HM Revenue and Customs say there was a rise from £33bn the previous year, partly the result of an increase of nearly a billion in the VAT shortfall and a widening of the tobacco tax gap.
It is the biggest overall gap in cash terms since 2009 and will add to concerns that some are managing to avoid tax in a time of austerity.
HMRC says causes include taxpayers simply not taking enough care with their tax returns and criminal attacks on the tax system.
It points out that the shortfall on the £500bn which should be brought in is much narrower in percentage terms than in 2006, at 6.8 per cent of tax owed compared with 8.5 per cent seven years before.
And that some other countries have much bigger shortfalls: Mexico's is in excess of 25 per cent.