Families with children where one parent works will be hardest hit by new tax changes that come into force on Saturday, according to shadow chancellor Ed Balls, who says gains from a higher personal allowance of nearly £10,000 are "swamped" by higher VAT and cuts to tax credits.

Balls said prime minister David Cameron had prioritised tax cuts for millionaires over "squeezed" workers after new figures from the Institute for Fiscal Studies (IFS) show that a one-earner family with children will lose an average of just under £4,000.

The thinktank's data shows that a couple with children, where one parent works, will be worse off by £3,995.65 a year on average after the tax and benefit changes introduced since 2010. Average households will be worse off by £891 a year.

Balls highlights a series of changes that will be introduced with the start of the new financial year. These include a freeze in child benefit for a third year and an increase in tax credits by just 1%. The personal allowance will increase to £9,440 although the higher threshold will fall to £41,450 to help pay for this.

Labour argues the figures show the government has the wrong priorities because the tax changes include a cut in the top rate of income tax from 50p to 45p. This will give 13,000 people who earn more than £1m an average tax cut of £100,000. The change will benefit 267,000 people earning £150,000-plus a year.

The shadow chancellor said: "These figures show the full picture David Cameron and George Osborne do not want you to see. They reveal that any gains ministers boast about from the rise in the personal allowance are swamped by higher VAT, cuts to tax credits and child benefit.

"People in work, people looking for work, stay at home mums and pensioners hit by the granny tax are all being squeezed like never before. Millions are paying more while millionaires pay less."

The IFS data shows that lone parents will also be hit by the changes. A lone parent in work will be worse off by £1,225.95 a year while a lone parent out of work will lose £1,206.50. Couples with children where both parents work will be worse off by £1,869.09 while a similar couple with no children will lose £672.10.

The coalition defended the tax changes on Saturday with David Cameron taking to Twitter to highlight the increase in the personal tax allowance. He wrote: "From today 24 million people will be paying £600 less income tax than in 2010."

Danny Alexander, the chief secretary to the treasury, told the Today programme: "My priority as the Liberal Democrat in the Treasury has been to deliver as fast as possible the big income tax cuts for working people and overall to ask the wealthiest to pay more. The wealthy are paying more in every year of this government than they did during the entire period Labour was in office."

Cameron also posted a link on Twitter a new Conservative poster outlining the change with the headline "Help for Hardworking People".

Labour launched its own poster – with the tag "Who Wants to Bung a Millionaire? Dave Does" – setting out claims that high earners are benefiting while millions are worse off under coalition reforms.

The personal allowance and top rate change are just some of the financial changes being implemented from April 6. The Daily Telegraph reported that the new requirements for the small businesses to inform Her Majesty's Revenue Customs (HMRC) of wage payments as they happen could be a damaging burden. Next week, the civil service union PCS will go on strike as HMRC introduces its real time information system which allows employers to update any payments they make as they make them.

Saturday's rise in the personal allowance will give an extra £267 a year to millions of basic rate taxpayers but has been paid for by reducing the threshold for 40% tax to £41,450, adding 400,000 people to that tax band.

Most tax credits and working age benefits, including Jobseeker's Allowance, are being increased by 1% – below the rate of inflation while pensioners get an increase in the state pension, which goes up by 2.5% to £110 a week.

The general secretary of the Unite union, Len McCluskey said the budget changes will only benefit the wealthy and will not energise the economy.

"This is not the way to recover our failing economy. Creating real jobs and paying decent wages, including a one pound increase on the minimum wage, will bring down the benefits bill and get people spending again," he said.

"Instead of getting on with the job he ought to be doing, like sorting out the problems he has caused to our economy, Osborne prefers to encourage hatred and demonise the poor, both in and out of work, in an ideological attack on our welfare state."

• This article was amended on 8 April 2013. The original said incorrectly that the Labour party had commissioned research from the Institute for Fiscal Studies. The IFS does not take commissions for research from any political party.