The south-west of England will have the highest proportion of low-income workers affected by a £20-a-week cut later this year in universal credit payments, according to analysis by the TUC that illustrates the widespread culture of low pay from Cornwall to Gloucestershire.

More than four in 10 universal credit claimants in the south-west have a low-paid job that qualifies them for benefits, a larger percentage than any other region, said the trade union body.

The rate of claimants who had a job in May was 42.1% in the south-west compared with 41.2% in the east Midlands, the next worst affected, and 36.7% in the West Midlands.

The TUC general secretary, Frances O’Grady, said 2.3 million working families, as well as those who rely solely on benefits, would see their incomes drop by more than £1,000 a year if the government presses ahead with a planned £20-a-week cut in universal credit from October.

The report also highlights the impact on individual parliamentary constituencies, revealing that the prime minister’s west London Uxbridge and South Ruislip seat has 9,546 UC claimants of whom 3,665 are in work, 38.4% of the total.

In the chancellor Rishi Sunak’s Yorkshire constituency of Richmond nearly half, 48%, of people receiving universal credit are in work.

The TUC said: “It shows that even in wealthier parts of the UK the cut to universal credit will impact heavily on low-paid workers.”

About 6 million families claim UC and its predecessor, working families tax credit – twice the figure before the pandemic. More than 500,000 people were forced to file a claim during just nine days in March 2020 as the virus began to spread and the government announced the first lockdown.

In the same month, ministers agreed a £20 rise in universal credit and tax credits as a one-year measure to help new claimants adjust to the extra costs of the pandemic.

Estimates suggest it helped 700,000 people stay above the poverty line during the pandemic. Surveys have shown the public support it being made permanent.

Earlier this month Thérèse Coffey told MPs the government had honoured its commitment to extend the uplift for six months. Now the economy was opening up, she said, the focus of DWP support “should be strongly on getting people into work and jobs”.

Although there was no up-to-date robust data showing that claimants were coming off the benefit in significant numbers, Coffey said internal DWP figures suggested there were 2.1 million job seekers on universal credit, down from 2.5 million in March, and this number was reducing week by week.

Labour, welfare charities and some Tory MPs have criticised the move, saying that millions of people will still be in precarious jobs in October and unable to cope financially after a cut in benefits of more than £1,000 a year.

In a separate report, also timed to coincide with the summer parliamentary recess, the Joseph Rowntree Foundation said more than 500,000 people, including 200,000 children, will be plunged into poverty when the government pushes through what it called “the largest single cut to the basic rate of social security since the second world war”.

About 6 in 10 of all single-parent families will experience their income falling by the equivalent of £1,040 per year after the benefit cut, it said, imposing “the biggest overnight cut to the basic rate of social security since the foundation of the modern welfare state”.