Sir Keir Starmer has defended Labour’s decision to rebrand its package of workers’ rights pledges following a backlash from one of the UK’s biggest trade unions.

The party leader denied he was weakening policies on areas like zero-hours contracts, parental leave and sick pay after Unite general secretary Sharon Graham said the plans had “more holes than Swiss cheese”.

It comes after the latest flare-up in a row over Labour’s New Deal for Working People, following reports it would go through a formal consultation process with businesses – potentially delaying or toning down the pledges.

On Friday, Labour rebranded the New Deal as “Labour’s plan to make work pay” as it released a final version of the plans.

During a visit to Staffordshire on Saturday, Sir Keir told the BBC: “We have come to an agreement with the trade unions on the new deal for working people.

“There’s been no watering down. This is the most significant set of protections for a generation.

“It’s also something which I think employers and good businesses would say, ‘looking at the detail of it, this is what we’re doing in good businesses’.”

Elements of the deal include a “right to switch off”, a proposed ban on “exploitative” zero hours contracts and stronger employment rights from day one of a new job.

The party has also said it wants to empower adult social care professionals and trade unions that represent them to negotiate a sector-wide agreement for pay, terms and conditions.

Several other unions have backed the plans, saying they represent a vital step towards better protections for employees.

But Unite suggested the wording had been softened, with a previous proposal to ban zero hours contracts revised to refer only to “exploitative” zero hours contracts.

Reacting to the recent rebrand, Ms Graham said: “The again revised New Deal for Working People has more holes in it than Swiss cheese. The number of caveats and get-outs means it is in danger of becoming a bad bosses’ charter.

“Working people expect Labour to be their voice. They need to know that Labour will not back down to corporate profiteers determined to maintain the status quo of colossal profits at the expense of everyone else. The country desperately needs a Labour government, but the party must show it will stick to its guns on improving workers’ rights.

“Fire and rehire is abhorrent and must be banned – no ifs, no buts. Unite will continue to call out any row backs on the New Deal for Working People, which was a promise made.”

However, Unison, which along with Unite is one of the two largest unions in the UK, welcomed the package in its current form as one that will “make work fairer and boost the economy”.

“There will be a clear choice in July: a vote for a party that understands the huge struggles employees and their families have been facing, or one that’s persistently let working people down these past 14 years. Labour’s new deal best illustrates that choice,” general secretary Christina McAnea said.

“That’s why its measures are proving popular on the doorstep. Bad employers will no longer be able to outprice good ones by cutting corners and reducing costs by exploiting staff.”

GMB also voiced support for the measures, with a spokesperson describing them as a “vital step towards righting the wrongs of 14 years of Conservative government”, while Usdaw general secretary Paddy Lillis said they were “the biggest offer any party has ever made to workers”.

A Labour spokesperson said: “Labour’s New Deal for Working People is our plan to make work pay. It’s how we’ll boost wages, deliver secure work and support working people to thrive – delivering a genuine living wage, banning exploitative zero hours contracts, and ending fire and rehire.

“The New Deal is a core part of our mission to grow Britain’s economy and raise living standards in every part of the country. Labour will make Britain work for working people.”