Foreign Secretary Dominic Raab has said the shift includes a greater emphasis on common strategic interests in the region, which goes beyond trade.
Jaishankar said the two ministers also discussed Indo-Pacific cooperation and global health challenges in some detail.
"By the time we get to June 21 almost all social restrictions will be lifted," Dominic Raab said.
Dominic Raab named India among the countries that would help address the need for diversified global supply chains with high trust vendors.
Raab had visited India last December and held talks with Jaishankar during which the two sides had agreed on the key elements of an ambitious 10-year roadmap to further broaden ties
Earlier today, Union Minister of Environment Prakash Javadekar also met Alok Sharma and discussed important issues, for negotiations to be held in Glasgow later this year.
Protests were held outside the Indian High Commission in London in support of the agitating farmers who have been demanding repeal of the newly enacted farm laws.
In a tweet after the meeting, Modi said he was looking forward to UK Prime Minister Boris Johnson's visit to India to be the Chief Guest at the Republic Day celebrations next month.
Currently, the UK’s one-year Master’s programme is not recognised in the public sector in India along with certain subject-specific hurdles in fields such as medicine and law.
On Tuesday, Raab met Minister of Environment, Forest and Climate Change Prakash Javadekar where he said that the UK will be working closely with India to tackle climate change.
His assertion of strengthening ties with India in a host of fields, including in the health sector, came after his talks with External Affairs Minister S Jaishankar.
Duing their wide-ranging talks, Jaishankar and Raab also discussed ways to enhance trade partnership which could be a stepping stone towards a future free trade agreement.
S Jaishankar and UK foreign secretary Dominic Raab hold talks, discuss ways of expanding cooperation
There have been apprehensions that its separation from the European Union without a trade deal could severely cripple its financial markets and may have long-term implications for its economy.
Liberal Democrat party leader Ed Davey said that while the agricultural reform policies are a matter of Indian domestic politics, the use of "militarised police" was of some concern.
The ministry said that Raab's visit will pave the way for further strengthening of the partnership across trade, defence, climate, migration and mobility, education, and health sectors.