At the same time, May said her government will consider further improvements to its visa offer to India if speed and volume of returns of Indians "with no right to remain" in UK is stepped up to which the Indian side conveyed that it will follow international practice and a proper verification process.
May while announcing the UK offer of two new visa services to improve business travel for Indians to the UK said that under the Registered Traveller Scheme, business travellers will get expedited clearance at the UK border and that India will become the "first visa country" under the scheme.
During the talks with May, Prime Minister Narendra Modi flagged India's concerns over stringent student visa norms which require students to return home after their courses end. The norms has led to fall in Indian students enrollment in British universities by 50 per cent.
The number of study visas issued to Indian nationals fell from 68,238 in 2010 to 11,864 this year, official UK figures show.
The contentious issue figured prominently during bilateral talks between Modi and May.
"We flagged our concerns regarding students visa issues, visa issues regarding business travellors and other issues relating to bonafide travellors to the UK," Joint Secretary (Europe) in the External Affairs Ministry Randhir Jaiswal told reporters.
The UK has also raised the threshold limit for salary from 20,800 pounds to 30,000 pounds to get work visa which is expected to impact the Indian companies, particularly those in IT sector.
He said India has been maintaining that it will go by verification at its own level.
Swarup wondered, "How can we accept them because there is
no DNA test which can prove (that) in the sub-continent everybody is the same."
Jaiswal said visa and mobility were "very important" subjects as far as India-UK ties are concerned.
In her press statement after talks with Modi, May said the UK will continue to welcome the brightest and best Indian students, with the latest figures showing that 9 out of 10 applications are granted.
She said both sides agreed to establish a strategic dialogue on home affairs issues covering visas, returns and organised crime.
"As part of this, the UK will consider further improvements to our visa offer if at the same time we can step up the speed and volume of returns of Indians with no right to remain in the UK," she said.
"This included ensuring the timely and efficient return of individuals to their country of origin, as required by their respective national laws.
"Both countries agreed to strengthen co-operation in this area by implementing an expedited process for verifying the nationality and issuing travel documents," the statement said.
While referring to the new visa programmes offered by the UK, it said the two Prime Ministers welcomed the "changes, which will mean that India will have one of the best UK visa services of any country in the world, with more application points than anywhere else and the only place where you can get a same day visa".
"To this end, both parties agreed that visa regimes need to be as simple and efficient as possible for students, businesses, professionals, diplomats and officials and other travellers, including facilitating short-term mobility of skilled personnel between the two countries," the joint statement said.
It said May noted that there remained no cap on overall numbers of international students studying at recognised educational institutions in the UK, that Indian students would continue to be welcome and that the UK Home Secretary had recently announced her intention to consult on changes to the UK student visa regime.
The joint statement said the two Prime Ministers announced the launch of a senior UK-India dialogue on Home Affairs issues which will take place bi-annually.
"The Prime Ministers expect this dialogue to make progress on key issues of mutual concern, including opportunities to make the visa system simpler and more efficient, and steps to improve the integrity of border and immigration systems," it said.
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