More than 2 million poor families will be more than £50 a week worse off by the end of the decade, according to an alarming analysis of welfare cuts, crippling rent rises and looming inflation.

In a bleak assessment of the plight of the poorest families in Britain, the study commissioned by the Local Government Association found that more than 84% of those set to lose £50 a week or more are households with children, either lone parents or couples. Almost two-thirds of them are working households, despite claims from ministers that they wish to create a welfare system that encourages work.

The analysis, by the Policy in Practice consultancy, also undermines claims from ministers that moves to cut taxes and increase the wages of the poorest are compensating them for years of austerity and the rising cost of living.

While some of the seven million low-income households in Britain will be better off by 2020, the group as a whole faces an average loss of £40.62 a week by 2020 compared with the end of last year, once benefit and tax changes, wages, housing costs and inflation are all taken into account.

The report’s publication comes as Philip Hammond, the chancellor, faces intense pressure to ease years of austerity following an election result that signalled voters had reached the end of their patience with spending cuts. Nurses took to the streets in protest last week over claims they have suffered a 14% real-terms cut in their wages over the past seven years. Hammond is also under pressure to curb rising levels of student debt in the forthcoming budget.

The study finds that the introduction of the government’s flagship policy of universal credit, which combines a series of benefits into a single payment, will lead to an average income loss of £11.18 per week. It coincides with new warnings from Citizens Advice that the rollout of the system should be halted, amid claims that some of those already receiving it have found themselves in serious debt.

With charities and councils warning of rising homelessness, increasing housing costs are identified as a main cause of falling income. More than 2 million low-paid private renters face an average real-terms loss of £38.49 a week by 2020.

A Tories out national demonstration against Theresa May earlier this year. Photograph: Matthew Chattle/Barcroft Images

For low-income private renters with three or more children, the average income loss that they face by 2020 in real terms is £67.21 a week. This compares with £30.67 for private renters without children.

The authors also say rents are rising faster in some areas than others, with housing benefit not rising to match it. The study found rents are set to rise by 20.7% in the south-west by 2020, but by just 3.5% in the north-east. The report warns that there is now a looming “affordability crisis” because cuts to housing benefit, known as local housing allowance (LHA) for private renters, mean it is no longer linked to real rents, pushing people into poverty or even homelessness.

Polly Neate, chief executive of Shelter, said: “This report reveals the true state of Britain, a country where millions of families face a daily struggle to afford a roof over their head and food on their table. This is the everyday experience of millions of people forced to the edge of homelessness.

“That’s why we’re calling on the government to act now, in this year’s budget, to end the freeze on housing benefit and to commit to building decent homes at affordable rents. Without this action this is a crisis which can only get worse.”

The study points out that funding handed to councils and targeted at helping poor families had also been stripped back.

Funding for extra help in the form of “discretionary housing payments” in 2017-18 is £185m, dwarfed by the combined annual income loss associated with the government’s benefit cap, the bedroom tax and those paying rent above housing benefit levels, totalling more than £4bn.

Claire Kober, chair of the LGA’s resources board, warned that the problems highlighted in the report came as councils were “experiencing huge funding pressures and faces an overall funding gap of £5.8bn by 2020”.

“Councils are particularly concerned by the potential rise in the number of households in temporary accommodation or at risk of homelessness,” she said. “With the right funding, freedom and flexibilities, councils could do so much more to manage and mitigate the impact of the welfare reforms, and help low-income households.”

The analysis also suggests the government’s attempts to increase the minimum wage and lower income tax on poorer workers is not helping those in most need. It found 4.8 million low-income households would see no net benefit from the measures.

Of the 2.4 million households that are better off due to the measures, 900,000 are households that are actually gaining from the transition to universal credit.

Deven Ghelani, director of the Policy in Practice consultancy, said: “The broken link between LHA rates and rents means that housing is becoming increasingly unaffordable for people, particularly within the private rented sector.”

The Department for Work and Pensions said: “This report assumes that people won’t make any attempt to change and to improve their lives. But our welfare reforms incentivise work and, for the first time, universal credit helps working people progress and earn more, so they can eventually stop claiming benefits altogether.

“Under universal credit people are finding a job faster and staying in it longer than under the old system, and since the benefit cap was introduced, 34,000 households have moved off the cap and into work.”