Oliver Letwin reported as saying discussion of uniform tax rate may 'open up' once public finances improve

The Conservatives would secretly like to bring in a flat rate of tax meaning rich and poor alike paid 31%, Ed Balls has claimed.

The shadow chancellor said the thinking of senior Tories had been exposed after Oliver Letwin, a Cabinet Office minister, was reported by the Daily Mirror to have been recorded mulling a flat tax when speaking at a thinktank.

"In 2010, indeed now, we were not in a position to take a large fiscal cut. There may come a time when the situation is different and that discussion will no doubt open up," he was quoted as saying.

Balls will claim in a speech that the Tories are first plotting to cut the top rate of tax to 40p after the next election, having previously lowered it to 45p.

Conservative sources denied that either of the moves were on the cards, rejecting the idea of a flat rate "full stop", as tax started to become a battleground for claims and counter-claims between the parties before the election.

A separate recording on Wednesday quoted Andy Burnham, the shadow health secretary, backing a tax on estates to pay for elderly care, while acknowledging there were questions over whether this was publicly acceptable. Labour said this was not the party's policy.

Previously, Labour has accused David Cameron of being a liar for taking comments made by the deputy leader, Harriet Harman, out of context to claim she would like to impose higher taxes on the middle classes.

Before a speech on the economy on Wednesday morning, Balls cast Labour as the party of fairer taxes as it would raise the top rate of income tax for those earning more than £150,000 to 50%.

"There's a very clear choice at the next election. We say, put the top rate back to 50p while we get the deficit down in a fair way. George Osborne wants to cut the rate to 40p. In fact, we now know from Oliver Letwin that they want a flat tax, cutting the top rate to 31%," he told BBC Radio 4's Today programme.

Balls will also set out figures from the House of Commons library showing that there will have been the biggest squeeze in income since the 1874-1880 parliament of the Tory prime minister Benjamin Disraeli. He will claim it is the first parliament since the 1920s in which real earnings have been lower at the end than at the beginning.

The economy is not fixed and most people are worse off under the Conservatives, he will say, pointing out that average wages after inflation are down by more than £1,600 since 2010.

"From a Conservative-led government that promised to make working people better off back in 2010, this is a dismal record of failure," he will say.

Listing the risks of a Conservative government to the economy, Balls will say the Tories would offer more depressed wages and no proper industrial strategy.

In contrast, Labour would balance the books in a fairer way while freezing energy bills, introducing a lower 10p starting rate of tax, increasing the minimum wage and offering tax breaks to firms that pay the living wage.

"This is the stark choice we face next year," he will say. "A choice between a Labour plan to make Britain better off and fairer for the future – with rising living standards for the many, not just a few at the top – or more of the same from the same-old Tories."

Balls's speech is the latest in a series from Labour on the theme of choice, highlighting the party's differences with the Tories. Ed Miliband contrasted his dislike of image-based politics with Cameron's career based on photo opportunities; Yvette Cooper, the shadow home secretary, attacked the government for turning its back on domestic violence; and Burnham called for a ban on further privatisation of the NHS.

Their speeches are designed to counter accusations last year that Labour left a political vacuum in the summer, allowing criticism of Miliband to fester among some backbenchers. It also marks an intensification of political attacks on the Conservatives with less than a year to go to the election.