Low-earning families that Theresa May has promised to help will be thousands of pounds a year worse off by 2020 because of rising inflation, lower wage growth and Tory social security cuts, according to new analysis of their post-Brexit economic prospects.

Those who the prime minister describes as “just managing” – and who are her key priority, she says – are in line for substantial falls in real incomes unless the chancellor, Philip Hammond, steps in to help them in his autumn statement on 23 November.

Pressure is growing on Hammond from senior Tories to reverse the decisions to slash benefits, which were announced last year by his predecessor George Osborne, in order to assist those who May said on entering Downing Street were “working around the clock” but still struggling to get by.

New analysis by the Resolution Foundation, which takes into account the latest official forecasts on earnings and inflation, and the effects of 2015 budget announcements on tax, the living wage and benefits, finds that an already gloomy outlook for these families has got markedly worse since Brexit.

It shows that a couple with two children both under the age of four, who are both working (one full-time at £10.50 an hour and the other for 20 hours a week at the living wage) will be £2,000 worse off in 2020 than would have been the case without the double hit from the effects of Osborne’s policies and the Brexit vote.

The foundation finds that a single parent with one child under the age of four, working full-time on the minimum wage, would in 2020 be £3,800 worse off as a result of measures announced in this parliament so far.

One important factor in these recalculations is that higher inflation and expectations of lower wage growth since the Brexit referendum have reduced the previous anticipated increases in the National Living Wage (NLW). Wherereas Osborne said the NLW would reach £9.00 an hour by 2020, the foundation says it now expects it to be only £8.60 an hour. The level of the NLW is linked to rises in the pay of typical workers. Millions of families are also affected by pay freezes across the public sector that will last until 2020, which will feel more severe as inflation rises.

Lord Willetts, the former Tory minister who is now executive chairman of the Resolution Foundation, said May was right to prioritise those who were “just managing” but faced a “pretty tough climate in which to do it. The chancellor faces a double headwind. One consequence of the big falls we have recently seen in the value of the pound is that prices will rise more quickly over the next few years. This will squeeze family budgets with higher prices in the shops, and turn the cash freeze in social security support for working age families into a significant and painful real terms cut.

Lord Willetts, the former Tory cabinet minister, now executive chairman of the Resolution Foundation which published the report. Photograph: Richard Gardner/REX/Shutterstock

“Added to this is the £3bn being taken out of the government’s flagship universal credit programme through cuts to in-work support. These cuts will reduce the incomes of ‘just managing families’ more than any other group. For many families, and for women in particular, these cuts will also reduce their incentive to work.

“Making progress in reversing the effect of the social security cuts inherited by the new government is not cost-free, and that matters given the £84bn borrowing black hole the Treasury is likely to face in [the] autumn statement. But the money can be found if the chancellor chooses to make it the focus of his autumn statement. That would send a powerful message that the government really is on the side of just managing families.”

Angus Armstrong, director of macroeconomics at the National Institute of Economic and Social Research, said: “Those millions of people Theresa May has promised to help are facing a series of challenges from rising inflation, benefit cuts and freezes as well as caps in public sector pay until 2020.

“Given the financial constraints on government post-Brexit it will prove difficult for ministers to deliver that help without radically departing from their previous approach which has been to balance the books. The problem is that the PM has made a laudable commitment but when she can least afford it.”

So far the Treasury has insisted that it will not revisit benefit cuts, including those to universal credit, despite calls from Tory MPs, including former work and pensions secretary Iain Duncan Smith, to do so.

Privately, however, Treasury officials are becoming increasingly concerned at the economic outlook and the chancellor’s resulting lack of room for manoeuvre. They fear that recent bouyant GDP figures will prove a high watermark for the economy before a period of stagnation in 2017.

The fall in sterling is proving helpful to exporters but is coming at the cost of higher import prices which are expected to push inflation to as much as 3% next year. With wages rising at around 2%, a hike in prices of this magnitude will eat into disposable incomes.

GDP figures covering the three months to the end of September revealed last week that most of the strength in the economy came in the services sector and consumer spending. The rise of 0.5% beat City expectations of a slowdown in growth to 0.3%. However, the manufacturing sector contracted and the construction sector fell into recession after two consecutive quarters of negative growth.

HSBC warned in the summer that the UK faced a period of stagnant growth and high inflation – stagflation – next year. Former Bank of England monetary policy committee member Adam Posen repeated the warning last week. Posen, now the head of the Peterson Institute thinktank in Washington, said Brexit had caused the UK permanent damage that would be made worse by higher inflation and slowing consumer demand, which would result in lower growth

Bank of England interest rate setters meet on Thursday to consider policy options that include cutting interest rates to support the economy as it heads into a period of lower growth or raise interest rates to choke off inflation. City analysts expect the Bank to sit on its hands and wait for more survey data to reveal the impact of the Brexit vote on business investment and consumer confidence.