The Treasury chief secretary, Danny Alexander, has defended changes to the tax system after figures were published saying that families with children stand to lose £511 a year on average on "black Friday".

In what is likely to be a key battleground in the local elections, the Treasury said the Institute for Fiscal Studies figures were partial, and it chose to highlight the impact of the lifting of the personal allowances for most basic-rate taxpayers.

Alexander said the government had made some "very difficult decisions" on tax and benefits but insisted they had been fair. He told BBC Radio 4's Today programme the government was still spending £31.6bn on tax credits, a £3.2bn cut in real terms.

"That is part of the package of measures that we have to take to deal with the catastrophic mess that Labour and Ed Balls left our economy in," he said.

The analysis, compiled for the Labour party, follows changes made in George Osborne's budget last month, which came on top of the introduction of tax increases such as last year's VAT rise, which is costing a family with children an average of £450 a year. The figures include the impact of raising the personal allowance.

Labour said more than 850,000 families on modest and middle incomes would lose all their child tax credit, worth about £545 a year. Up to 212,000 working couples earning less than £17,000 a year will lose all of their working tax credit – worth up to £3,870 a year – if they cannot increase their working hours. It is the first time the IFS has put these calculations in cash terms.

According to Labour, a couple with two children on the minimum wage will be better off quitting their jobs if they cannot work at least 19 hours a week.

Balls, the shadow chancellor, accused the government of giving with one hand and taking much more away with the other.

"For all the government's talk about increasing the personal allowance, these independent figures show that, while they may be giving with one hand, they are taking much more away with the other. That is why families with children will be an average of £511 a year worse off from tomorrow," he said.

The two main changes to tax credits are a reduction in the income limit for child tax credit, from about £40,000 to about £26,000 for a family with one child, and an increase in the number of hours couples with children have to work to be eligible for working tax credit, from 16 to 24 hours a week.

Challenged about the difficulties facing couples on working tax credits, Alexander said: "Of course, I recognise these are very difficult decisions we have had to make."

But he added: "When you look at the overall impact of the tax changes, the benefit changes and the spending reductions we have had to make to deal with Labour's economic mess, the burden of that falls most heavily on the top 20% of the population.

"But of course the burden of that does fall across the population, less on lower incomes than on the highest incomes, but still difficult in those situations.

"I think it is right to say… if you are going to ask a single parent to work two days a week before they can receive working tax credit, I think asking a couple to work three days a week between them is a reasonable position.

"And when you take into account too the fact that 24 million people are benefiting from income tax reductions, delivered by this coalition government, that came from the Liberal Democrat election manifesto, I think that is a fair position which encourages and incentivises work, which, after all, must be the purpose of the tax and benefit system."

Labour said research by the House of Commons library showed the gain to basic-rate taxpayers from the rise in personal allowance above normal indexation (ie the real-terms gain) was £42 a year, or 81p a week.

The Treasury countered that 24m households would be £6.50 a week better off from government action, including the increased personal allowance, a rise in the basic state pension and increases in other benefits.

"Even taking into account changes to tax credits, the average household will be £5.50 a week better off in cash terms – with more than 15 times as many gaining than losing," the Treasury said.

"Around 24m households will benefit and around 1.4m will lose from modelled tax and benefit measures coming into effect this week – so more than 15 times as many will gain than will lose," the Treasury said.

Separately, the Resolution Foundation, a thinktank aiming to improve living standards for people on low and middle incomes, said thousands of working families would lose up to a quarter of their household income from Friday.

It said a young couple working 23 hours with one child and a household income of £15,500 would have received nearly £6,000 this year in working tax and child tax credits.

From Friday their entitlement to working tax credits would be switched off. Even taking into account the increase in the personal allowance and a small increase in child tax credits, the family is still projected to lose £2,961 a year (about 19% of total income) as the gains are offset by the wages squeeze and frozen child benefit.

The impact is greater the less income households have, as they have more working tax credits to lose. A single earner on the minimum wage of £6.08 an hour, working 20 hours a week, will lose £3,910 – more than a quarter (27%) of their income.

• This article was amended on 5 April 2012. The introduction stated that up to 1 million families with children stood to lose £511 a year. This average figure from the IFS applies to all families with children. The tax credit losses are separate and apply to up to 1 million families. This has been amended.