Large UK retailers including Tesco, Boots, Marks & Spencer and Next have written to Rachel Reeves to say that a £7bn increase in annual costs after last month’s budget would lead to job cuts and higher prices.

The letter, with 79 signatories sent by the industry body the British Retail Consortium (BRC), warns the chancellor of the financial impact of the impending increase in the national living wage and employer national insurance contributions (NICs).

The BRC has said absorbing the impact of the higher costs will mean higher prices for consumers, smaller pay rises, job cuts and store closures.

“For any retailer, large or small, it will not be possible to absorb such significant cost increases over such a short timescale,” the letter says. “The effect will be to increase inflation, slow pay growth, cause shop closures and reduce jobs, especially at the entry level. This will impact high streets and customers right across the country.”

The letter says retailers are already starting to make “difficult decisions” and “the sheer scale of new costs and the speed with which they occur create a cumulative burden that will make job losses inevitable, and higher prices a certainty”.

Nick Stowe, the chief executive of Monsoon and Accessorize, said retailers had been left with the choice of protecting staff numbers or cancelling their investment plans.

The fashion retailers’ boss told BBC Radio 4’s Today programme: “We’re trying to protect that staff number and it’s about choices in how we protect it.

“For us it means passing on some of those cost increases in terms of increased prices. It also means we’re probably going to have to divert investment that we would have made in growing our store base into protecting the stores that we have and the employees that we have.”

He added that the decisions businesses were being forced to make seemed “entirely counter” to the government’s proclaimed growth agenda.

On Tuesday, the beleaguered luxury handbag maker Mulberry said the UK market had been hit particularly badly from low consumer confidence, as it announced that it intended to cut jobs.

The signatories to the BRC letter also include the B&Q owner Kingfisher and the supermarket chains Morrisons and Sainsbury’s.

The BRC estimates that retailers will face a £2.3bn bill from April after the implementation of the increase in employer NICs from 13.8% to 15%, as well as the reduction in the earnings threshold that they must start paying it from £9,100 to £5,000.

Retailers said these changes would be felt in particular by retailers because they employed “large numbers of people in entry-level and part-time roles”.

In addition, retailers estimated that there would be a £2.73bn increase in wage costs from April, and about £2bn relating to an extension of producer responsibility for packaging from October.

The letter calls for a discussion with the Treasury to address some of the companies’ concerns, and offered solutions including a phased introduction of the new lower earnings threshold on national insurance (NICs), and a delay on the start of the levy on packaging.

Earlier this month, the bosses of more than 200 of the UK’s largest restaurant, pub and hotel businesses – including the Premier Inn owner Whitbread and Mitchells & Butlers – wrote a letter to the chancellor warning of closures and job cuts as a result of the rise in NICs.