Hospitality businesses will be forced to close while others will have to slash jobs and investment as a result of changes to national insurance announced in the budget, according to a letter to the chancellor signed by the bosses of more than 200 of the UK’s largest restaurant, pub and hotel businesses.

The letter – with signatories including the Premier Inn owner Whitbread and pub and restaurant group Mitchells & Butlers – comes as reports suggested Tesco would face an additional £1bn in costs over the course of the current parliament as the result of the increase in employers’ national insurance contributions (NICs).

The annual bill for the supermarket chain, which has 300,000 UK staff and is the country’s largest private employer, would be £250m, according to analysis from the US bank Morgan Stanley, which was first reported by the Sunday Times.

Hospitality businesses are warning that the sector will be hit by an additional £3.4bn in costs as a result of the budget changes, according to the letter to Rachel Reeves, signed by the bosses of companies including the pub operator Fuller’s and Stonegate Group, owner of the Slug & Lettuce chain, as well as Whitbread and Mitchells & Butlers, who all sit on the board of trade body UK Hospitality.

The signatories are cautioning that this will inflict “unprecedented damage” on the sector and force them to raise prices by 6% to 8%, although they say customers are not able to pay more.

“The changes to the NICs threshold are not just unsustainable for our businesses, they are regressive in their impact on lower earners and will impact flexible working practices which many older workers and parents rely upon,” the letter states.

“Unquestionably they will lead to business closures and job losses within a year.”

In addition, the leaders warn the changes will lead some businesses to reconsider their investment plans, while others will reduce hours for staff members, and contract catering firms will “struggle” to fulfil public sector catering contracts for schools, hospitals and prisons.

The government is expecting to raise £25bn a year from the changes to national insurance, making it the biggest single tax-raising measure in the budget.

Hospitality businesses warn that they are disproportionately affected by changes in October’s budget to employment costs. The lowering of the threshold at which employer NICs are paid to £5,000 will affect thousands of part-time staff for the first time.

The letter adds: “The threshold change brings many team members into employer NICs for the first time. We estimate the threshold change may be four times the cost of the new headline rate.”

The letter’s signatories – who also include the bosses of the Greene King pub chain, Wagamama owner The Restaurant Group and pub group Marston’s – are calling on Rachel Reeves to “consider measures to protect businesses who employ lower earners”.

They are asking the government to create a new band of NICs for those earning £5,000 to £9,100, which would have a lower rate of 5%, instead of 15%, or to bring in an exemption for lower-band taxpayers who work fewer than 20 hours a week.

The warning from pub, restaurant and hotel operators comes after large retailers including Asda, Sainsbury’s and Marks & Spencer shared their calculations of the annual cost of the budget measures to their businesses and warned of possible price rises.

Sainsbury’s said it would have to pay £140m more next year in NICs, likely leading to price inflation, while Asda put its own cost at £100m, and Marks & Spencer said it would have to pay £60m more next year.