Official estimates indicated £11.4bn of VAT, £15.3bn of income tax, £4.7bn in corporation tax and £2.5bn excise duties was not collected in 2011/12.
The HM Revenue and Customs' (HMRC) figures suggest £5.1bn was lost to the Exchequer as a result of evasion, £4.7bn as the result of criminal activity including fraud and smuggling and £4bn through avoidance schemes.
The £35bn estimated uncollected tax is an increase of £1bn from the figure in 2010/11, although the percentage tax gap decreased from 7.1% to 7%.
Exchequer Secretary David Gauke said HMRC would continue to "fiercely" challenge tax dodgers.
He said: "These figures show the tax gap is continuing to fall. The vast majority of businesses and individuals pay the taxes they owe.
"But where they don't, it is for HMRC to challenge non-compliance fiercely, protecting money that would otherwise be lost.
"Since 2010, the Government has invested nearly £1bn in additional compliance initiatives over the Spending Review period.
"HMRC is on track to secure a further £44bn in tax revenues over the next two years."
But Labour's Shadow Exchequer Secretary, Shabana Mahmood, said: "These figures show the Government is failing to tackle tax avoidance."