Britain and India have agreed a long-desired trade deal that ministers said would cut tariffs and add £4.8bn a year to the UK economy by 2040.

The agreement, which was finalised on Tuesday after more than three years of negotiations under successive governments, has long been touted as one of the biggest prizes of Brexit.

Keir Starmer said the “landmark deal” with India would “grow the economy and deliver for British people and business” after a call with the Indian prime minister, Narendra Modi.

The deal promises a boon for the UK’s car and alcohol industries, which have suffered from the impact of Donald Trump’s tariffs in the US.

However, it has caused a row over a decision to exempt Indian workers who have been temporarily seconded to the UK and their employers from national insurance contributions (NICs) for three years.

Kemi Badenoch, the Conservative leader, called it a system of “two-tier taxes”. The decision has also been criticised privately by some Labour MPs, given that NICs for UK employers have just been raised.

The agreement, which is reciprocal and will apply to British workers temporarily seconded to India by companies with offices in both countries, was one of Delhi’s key asks in the deal and one of the longest-running sticking points up until last week. The Indian government described it as a “huge win” and “an unprecedented achievement” for its side.

Yvette Cooper was not informed about the government’s plans to make it cheaper for Indian workers to come to the UK as part of the free trade agreement, the Guardian has learned.

The home secretary was left in the dark over controversial elements of the agreement which will mean Indian workers and companies avoiding national insurance, even as those on British employers are being hiked.

Home Office officials are said to have been confused by the process of agreeing the deal, having expected to be informed about anything which could increase migration to the UK.

Jonathan Reynolds, the business and trade secretary, defended the move and told reporters that some people were “getting a little bit carried away as to what this actually means”.

“We have 17 of these agreements with the EU, with South Korea, with the US and a whole range of partners, and what it is about is making sure when people are inter-company transfers between the UK and India – so for our people in India and Indian people in the UK – they don’t simultaneously pay into both social security systems,” he said.

A Labour spokesperson also said Badenoch was “desperately seeking to distract from her failure with a made-up row about a standard tax agreement that will benefit British workers abroad”.

“This deal will provide an annual £4.8bn boost for British businesses, create more jobs, raise wages by more than £2bn a year and bring down prices for hard-pressed consumers,” they added.

Badenoch’s criticisms were also contradicted by several senior Tories who praised the deal. Oliver Dowden, who was deputy prime minister under Rishi Sunak and is still an MP, welcomed the news, writing on X that it “builds on significant progress made by [the] previous Conservative government”.

Steve Baker, who dealt with trade as a Brexit minister under Theresa May, wrote: “This deal is great news. It further cements the path which I and others worked so hard to secure … the tax issue will likely turn out to be a red herring.

“We should be celebrating that a Labour government has furthered free trade in the national interest outside the EU.”

The deal is focused on tariff reductions for British and Indian goods across almost all sectors. India’s tariffs on British whisky and gin will be halved from 150% to 75% before reducing to 40% by the 10th year of the deal.

Tariffs on British cars will be reduced from about 110% to 10%, with quotas set on the number of British cars that can be exported to India and vice versa.

India will cut tariffs across 90% of British product lines, including cosmetics, lamb, salmon, soft drinks, chocolate and biscuits, as well as medical devices, aircraft parts and electrical machinery. Based on 2022 figures, the tariff cuts will be worth £400m from the day the deal is implemented.

The UK will lower tariffs on Indian clothes, footwear and food products. Ministers said this would give consumers access to cheaper products and more choice.

Parallel talks to agree a bilateral investment treaty, which would establish legal protections for investments between the UK and India, have not yet reached resolution. As a result, the deal does not include the financial services or legal services sectors. The Law Society called it a “missed opportunity”.

The deal does open up access for service firms to some Indian markets, including government procurement. It also involves reforms to customs procedures and rules of origin, allowing goods assembled in Britain to benefit from lower tariffs.

Modi and Starmer are expected to meet in the coming months to sign off the deal before it is ratified by the two countries’ respective parliaments.

Modi tweeted on Tuesday that India and the UK have “successfully concluded an ambitious and mutually beneficial free trade agreement” and that he was looking forward to welcoming Starmer to India soon.

Officials said that by 2040 the deal would increase bilateral trade between the UK and India by £25.5bn, the UK’s GDP by £4.8bn and wages by £2.2bn each year. British negotiators said it was the most ambitious deal ever agreed by India.

Officials said the deal involved no change to immigration policy but would facilitate visa routes for Indian professionals in certain sectors, and allow up to 1,800 visas for Indian chefs, musicians and yogis a year.

There will be no exemption from the UK’s forthcoming carbon tax, although talks on this continue. There will be chapters on anti-corruption, gender equality, and environmental and labour standards.

Reynolds held talks with his Indian counterpart, Piyush Goyal, in London on Tuesday last week, where the majority of outstanding issues were agreed.

After a brief trip to Norway, Goyal returned to London and met Reynolds before returning to India. The pair agreed the final elements while walking in Hyde Park together on Friday. Negotiators have worked round the clock over the weekend to finalise the agreement.

Reynolds relaunched the negotiations with India on a trip in March to Delhi, where the two sides agreed not to reopen the chapters agreed under the Conservatives.

A Home Office spokesperson said: “The business secretary has led on negotiating this important trade deal. As you would expect, on a trade deal of such breadth and complexity, wide ranging discussions to have taken place right across government, with many departments, including the Home Office, involved.”

The deal, which is the biggest and most economically significant trade deal the UK has done since leaving the EU, was pursued by a succession of Conservative prime ministers.

Boris Johnson and Liz Truss both set Diwali deadlines to reach agreements but failed to get them over the line. Under Rishi Sunak, negotiators got close to finalising a deal but this was put on ice when the UK election was called.

Reynolds said: “By striking a new trade deal with the fastest-growing economy in the world, we are delivering billions for the UK economy and wages every year and unlocking growth in every corner of the country.

Mark Kent, the chief executive of the Scotch Whisky Association, said it was “a once-in-a-generation deal and a landmark moment for scotch whisky exports to the world’s largest whisky market”.

He said it could increase scotch whisky exports to India by £1bn over the next five years and create 1,200 UK jobs.

Keshav R Murugesh, the chair of the Confederation of Indian Industry UK Business Forum, said the deal was “particularly important in a world where trade tensions are on the rise” and would help shield the British and Indian economies from external shocks.