India and the UK will press ahead with talks on a bilateral free trade agreement, Boris Johnson and the Indian premier, Narendra Modi, have said, after the UK made clear it was willing to make immigration part of any deal. The pair appeared to differ on how rapidly an agreement could be made – Johnson suggested it could be ready by the festival of Diwali in late October, but Modi pointed to the end of the year. Johnson said: “As the next round of talks begin here next week, we are telling our negotiators, get it done by Diwali in October.” Modi said there had been “good progress and we have decided to make all efforts to conclude the FTA [free trade agreement] by the end of this year”. Three rounds of talks had already been held. Johnson and Modi were speaking together at Hyderabad House in Delhi, where they were holding bilateral talks, as Johnson’s two-day visit to India draws to a close. Downing Street had hoped the trip would demonstrate the prime minister’s determination to focus on investment, jobs and security, but it has been overshadowed by events at home. On Thursday, Johnson’s allies were unable to prevent MPs supporting an investigation into whether he misled parliament over Partygate, and the senior MP Steve Baker, a former Johnson supporter, joined the ranks of those calling for him to go. India had been keen to make increased access to the UK for its citizens part of any trade agreement, and Johnson signalled on Thursday he was willing to make concessions in this area – something previous UK governments had refused to do. Asked whether he was willing to offer more visas as part of a deal, he told ITV: “The UK actually has a massive shortage in some sectors like IT. Some estimates say we are hundreds of thousands of people short. So what you can have is controlled migration, which allows you to bring in talented people who can really help your economy. He added: “We won’t give these things away lightly – we want to make sure we get a proper deal. There is room to do a fantastic deal.” The UK hopes its car industry and food and drinks manufacturers could benefit if tariffs are lowered under a deal. The government is under pressure to deliver further trade deals, with the hoped-for post-Brexit deal with Washington on the backburner as the US president, Joe Biden, focuses on other issues. Johnson had promised to raise difficult issues with Modi, including India’s ambivalent stance on Ukraine – though Johnson said en route to India that it was important to acknowledge the country’s longstanding relationship with Russia. Delivering a statement alongside Johnson, Modi called for an “immediate ceasefire” in Ukraine, and emphasised the importance of diplomacy, but did not criticise Russia, which is India’s biggest supplier of arms. India has abstained from successive UN motions condemning Russia, and continues to buy Moscow’s oil. The Russian foreign minister, Sergei Lavrov, met Modi in Delhi earlier this month, and insisted the two countries would continue to find ways to trade, despite western sanctions on Russia. The UK announced during Johnson’s visit that it would liberalise arms exports to India, as the countries deepen their cooperation of defence. The government will issue an open general export licence for India, which will mean separate licences are not needed for individual contracts.