Speaking to reporters at the India-UK tech summit, in Delhi, May said: “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.”

Acknowledging that nine out of ten visa applications are already accepted from India, “we have, I believe, a good system,” she commented.

“Education is vital for our students and will define our engagement in a shared future”

While May also reiterated that there remains no cap on overall numbers of international students studying in the UK, the number of Indian students in the UK has been falling.

The number of study visas issues to Indian nationals in the year to June 2015 was 11,864, a significant decrease from five years ago, when the number was as high as 68,238.

India has been calling for a less restrictive visa system for its nationals to study in the UK.

At the tech summit, Indian Prime Minister Narendra Modi said the two countries should “encourage greater mobility and participation of young people in education and research opportunities”.

“Education is vital for our students and will define our engagement in a shared future,” he said in his speech.

Both prime ministers welcomed the news of 198 new UK-government funded GREAT scholarships, for Indian students to come to the UK to study at 40 universities.

They also welcomed the first 35 UK faculties visiting India under the Global Initiative for Academic Networks programme, funded by the Ministry of Human Resource Development.

Despite her firm stance on the visa system, May announced India will be the first country to be part of the registered traveller scheme, which aims to speed up the process at airports for visitors entering the UK.

“That means for Indian nationals who frequently come to the UK – and who fuel growth in both our countries – the entry process will become significantly easier,” she announced.

“Fewer forms to fill out, access to EU/EEA passport control, swifter passage through our airports.”

This year has already been marked by both countries as the India-UK year of education, research and innovation.