Britain's increasingly hostile tone on migration risks creating a perception among students that it is not a welcoming country to study in, the vice-chancellor of Cambridge University has said.

Making a passionate defence of the value of immigration, Professor Leszek Borysiewicz said he opposed "crude" numerical limits on migrants, and praised Britain's plural society as one of its greatest strengths.

In an interview with the Guardian, Borysiewicz said that Cambridge had not been affected by falling applications, but cautioned that there was an emerging perception, particularly in India, that Britain was not welcoming. He said: "When I think of how my parents were welcomed to this country, I find that actually quite saddening. I do feel we are an open, democratic country and we should be setting the standards for the rest of the world, not hindering them."

The numbers of students to all universities coming to the UK from India fell by 38% between 2011 and 2012, and those from Pakistan by 62%.

The Welsh-born son of Polish refugees who found sanctuary in Britain after the second world war, Borysiewicz said he "abhorred" the idea of a strict net migration target, set by ministers at 100,000 a year, saying numbers "hide the true potential benefit that people coming to Britain can actually have".

His work at Cambridge – on Monday ranked as Britain's leading university in the 2015 Guardian University guide – and previously at institutions including Imperial College London had shown him that "many of the most inspiring applicants come from children of immigrant parents" who often valued education highly.

Borysiewicz also urged a greater recognition of the value of bilingualism among first- and second-generation immigrant children, and warned that the decline in learning languages in the UK could limit the educational and career chances of poorer children. He said that German teaching in particular was disappearing from schools in Britain, and blamed the decline in language learning on the global dominance of English, combined with British "laziness" over picking up languages.

Borysiewicz said that while Cambridge still received "huge numbers" of language degree applicants with very high grades, the university had seen declining interest in the subject. Applications have fallen from about 580 in 2010 to 380 for 2014, so that the ratio of applications to offers in modern and medieval languages is now almost two to one, well below the average across all courses at Cambridge, at five to one. The vice-chancellor said: "My concerns are that the biggest falls in application rates … are still in modern languages, and I think that is a problem, particularly in an international world."

Despite studies warning of the negative economic consequences of Britain's dire record on language learning, modern language study in England is in dramatic decline. Numbers taking A-levels in French and German fell 9.9% and 11.1% respectively last summer compared with the previous year. Though Spanish went up 4.1% last year, between 2008 and last summer entries for the three languages collectively plummeted 17.8%.

At university level, the picture is worse still: applications for non-European modern language degrees fell by 37% in the three years to 2013, and European languages by 17%.

The vice-chancellor's clarion call for an outward-facing, open-door Britain, comes amid heightened debate over immigration, sparked by the triumph of Ukip in the European elections. Interviewed before the elections, Borysiewicz added a powerful voice to those calling for a positive view of immigration. He also echoed calls from other vice-chancellors for Britain to remain within the EU, arguing that between 15% and 20% of major UK universities' research income now came through Brussels.

"The whole academic sector brings back more to the UK than the resource that Britain puts into these areas. These are very important sources of funding for our top institutions in this country and therefore Europe is a very important component part for a university such as Cambridge."

Borysiewicz, 63, was born and grew up in Cardiff and spoke only Polish until he went to school, where he quickly learned English. "My parents made very clear from almost day one that they felt the future for my sister and myself was very much in Britain," he said. The new wave of Polish families arriving in the UK over the past decade, since Poland joined the EU, were also, in the main, similarly "establishing those roots to be accepted within society", he said.

"One of Britain's greatest strengths has been in the way it has assimilated so many different communities, and we are a very plural and open society."

Despite opposition from universities, international students are included in the government's net migration target. Labour has indicated it may change the policy. Borysiewicz said he was "in global competition" for both students and staff, and opposed migration targets not only for students but in general.

"A university such as Cambridge competes with Princeton, Harvard, Stanford, much more so than other UK universities, and therefore anything that prevents us getting the very best students I believe would be to the long-term detriment of the United Kingdom.

"At a personal level I abhor the idea that we actually have a very strict migration target. There are so many nuances to numbers in this regard that it actually hides the true potential benefit that people coming into Britain can have. We should be looking at the capacity of individuals to contribute to our society here rather than have a political ding-dong over 'we brought in 10,000 fewer than you did'."