Thinktank claims that not even half of the austerity measures mentioned by the prime minister would be implemented by 2015

David Cameron has been accused of getting his sums wrong, after appearing to suggest the government had already made most of its proposed spending cuts.

The Institute for Fiscal Studies (IFS) said not even half of the austerity measures would be implemented by 2015.

Cameron wrote in the Times on Thursday: “In this parliament we will have made £100bn of savings while cutting income tax by £10.5bn. In the next parliament we plan to make £25bn of savings while making £7.2bn of income tax cuts.”

But the IFS said the figures were not comparable. The thinktank said only part of the 2015-2020 period was included and cuts proposed for 2015-16 had been included in the present parliament. It added that the figures relied on different measures that ignored the impact of other pressures.

“To say that there have been ‘savings’ of £100bn over this parliament is a useful and interesting statement if one is clear about what it means (and takes account of the fact that it includes savings planned for 2015-16),” the IFS analysis said.

“It is also interesting and useful to say that £25bn of ‘savings’ are planned over the next parliament (or at least for the years 2016-17 and 2017-18). But it is not useful to use those two numbers together to suggest that the vast majority of the planned cuts have happened. They haven’t.”

The thinktank added: “We think total spending will fall by about £28bn over the next parliament compared with about £23bn of spending cuts which will have been implemented by the end of this parliament. We are just under halfway there.”

The same Times article has also prompted Labour calls for the statistics watchdog to investigate claims that the Conservatives’ proposed tax plans will save the average worker £3,800 by 2020. In the article Cameron he suggested that governments have a moral duty to lower taxes.

“Let people keep the money they earn,” he wrote. “What is morally wrong is government spending money like it grows on trees. Every single pound of public money started as private earning.”

But in a letter to the UK Statistics Authority, Chris Leslie, Labour’s Treasury spokesman, said Cameron’s tax figures were misleading because they did not take into account reductions in tax credits and a rise in VAT. He said that his claims had also been based on “mythical assumptions” about Labour’s tax plans.

“David Cameron will be judged on his actions, not his words. He’s raised taxes 24 times. While millionaires have been given a huge tax cut, ordinary working people are paying more because he raised VAT and cut tax credits,” he said.

“Independent figures from the Institute for Fiscal Studies show that by next year families will be £974 a year worse off because of tax and benefit changes since 2010. And David Cameron still won’t rule out raising VAT again on families and pensioners to pay for £7bn of unfunded tax promises.”