A source told Sky News that "tricky" issues have not yet been resolved as the talks enter their twelfth round, almost a year after a deadline announced by Boris Johnson.

Government insiders say a full trade agreement being struck in time for Rishi Sunak's first official visit to India in September for the G20 summit is unlikely, despite "passion on both sides".

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"It's about the deal and not the date. There are several outstanding issues, and you leave the really tricky stuff until the end," a UK government source said.

A breakthrough in talks is not impossible, insiders said, but after criticism from ministers of the UK's deal with Australia, they say officials are not working to a deadline.

These difficult issues are understood to include relaxation of visa rules for Indian workers - as well as continued wrangling on trade standards.

Ms Badenoch will attend a meeting of G20 trade ministers in Jaipur and then head to Delhi to meet with industry minister Piyush Goyal.

While in Delhi, she will also meet the chairman of Tata group Natarajan Chandrasekaran, to discuss the company's investments in the UK including the steelworks at Port Talbot in South Wales.

A deal with India, which would be the largest bilateral post-Brexit trade deal the UK has struck, was one of Ms Badenoch's key priorities as trade secretary. Progress is understood to have been made on agreements to reduce prohibitive import tariffs on cars and whisky - to open up opportunities for British firms.

India is predicted to be the world's third largest economy by 2050, and the UK government estimated in 2019 that a trade deal could increase UK GDP by around £3.3bn by 2035.

MPs were critical of the announcement by Boris Johnson, who promised last April that a deal would be signed "by Diwali", an Indian autumn festival that occurred last year in October. The deadline has long passed.

Ms Badenoch said in December, when embarking on an earlier round of negotiations, that an "amazing" deal was possible, but she had no plans to discuss if student visas were part of it. Time-limited visas for highly qualified workers were under discussion, she told a newspaper.

Her trip last year was billed as a reset for negotiations. Home Secretary Suella Braverman was said to have set back the talks when she said in an interview last year that she had "concerns about an open borders migration policy with India" and pointed out that "the largest group of people who overstay [their visas] are Indian migrants".

Speaking to Sky News, Labour's shadow chief secretary to the Treasury, Pat McFadden, said his party would not rule anything out when asked if they opposed more visas being given to India.

Shadow trade secretary Nick Thomas-Symonds said: "The Conservatives' record on trade negotiations has been to deliver bad deals or no deals at all.

"They committed to delivering agreements with India and with the United States by the end of 2022, yet failed to meet their own deadline. So them trumpeting the latest round of trade talks falls far short the concrete action needed to get any deal across the line.

"India is a key partner for the UK, we have deep historical links and it is a fast-growing economy, so Labour is committed to deepening our trade links."

Mr Sunak's appointment as prime minister last year triggered great interest in India, with the TV station NDTV greeting it as an "Indian son rises over the Empire".

With both he and Narendra Modi expecting to face elections next year, a government source said there was "genuine passion on both sides" for a deal to come together.

Recent reports in India have suggested a deal is closer than UK officials say. Indian commerce secretary Sunil Barthwal claimed in the summer that it could be signed "well before" the end of the year.

It would be India's first free trade deal with a developed country, after an interim pact with Australia last year. Long-running talks have been held with the EU and US on trade.

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A Department of Business and Trade spokesperson said: "The UK and India are committed to working towards the best deal possible for both sides. We've made good progress in closing chapters, and are now laser-focused on goods, services, and investment.

"While we cannot comment on ongoing negotiations, we are clear that we will only sign when we have a deal that is fair, balanced, and ultimately in the best interests of the British people and the economy.