One of Britain's leading science personalities has said government plans to cut hundreds of millions in science funding and grant provision to poorer students are "nonsensical".

Professor Brian Cox said that proposals by the Department for Business Innovation & Skills (BIS) to slash science funding by £215m over two years and convert £350m of student grant payments into loans would damage a national priority.

"The future of our economy essentially rests on an investment in students … Virtually every [developed] country in the world knows that," Cox said.

Recently revealed by the Guardian, the swingeing budget measures that are expected to take effect from next year have in part stemmed from over-expenditure on supporting students in the private college sector – a cost which has trebled in the last year to £175m.

On Tuesday night, the department confirmed that it had initiated a leak enquiry after high-level documents detailing rangeing financial measures, some of which are awaiting approval from Nick Clegg, were passed to the Guardian.

Cox said that if the measures were the result of a budget "cock-up" – with millions more diverted to private colleges than expected – then it would be wrong to divert resources away from a "national priority".

"Policy should operate for the good of the country … the decision has been made at a high level, correctly in my view, that science and research in general and higher education should be a priority."

"George Osborne... [David] Cameron, [David] Willetts, Vince Cable, everyone agrees that investment in higher education is considered a priority. Everybody agrees that. So when you make accounting errors even of this scale, then … it shouldn't be the case that you say to BIS: 'Well, it's your cock-up, you deal with it.'

"We're talking about a national strategy … and that's the language that's been used … Once you've said that and once you accept it, then if you making an error in another area, then it's a cross-government problem … it's not a single department's problem … this is a national strategy."

Former Labour minister Alan Milburn, the coalition's current social mobility adviser, warned the grant cut could deter the poor from getting a degree.

Milburn said that restoring student grants had been part of the coalition deal that allowed parliament to treble tuition fees in 2010.

"A reasonable level of student grant was supposed to remove any financial barriers for lower income youngsters from applying to university," he said.

He added that "even before any proposed cut in the value of the grant there has been a big drop in mature and part-time students applying to university".

"The risk is that this proposal increases confusion and ends up deterring the very cohort of students ministers say they want to attract into higher education," he said.

Labour said it would table a series of parliamentary questions to discover what ministers knew and when, and whether they were warned about the risks of students at private colleges "soaking up" public subsidies.

Shadow higher education minister Liam Byrne added: "Ministers must confess now if they were warned that their free market experiment would damage Britain's public universities.

"We cannot have a situation where science and students are forced to pay the price for a toxic combination of dogma and incompetence."

One of the most outspoken student critics of the government, the president of the University of London Union (ULU), Michael Chessum, said that students were facing a debt-ridden future and called for students to organise protests against the plans.

"These cuts are the result of a government that cares nothing for public, accessible education and everything for an ideologically driven and chaotic market model – implemented with some truly spineless Lib Dem co-operation.

"The future that our education system is facing is debt-ridden, marketised and exclusive, and we must organise a national-level movement to prevent nightmares from becoming a reality."

Lobby group Science is Vital said it was extremely concerned by the reported budget plans and said it would fight any attempt to drop the government's commitment to a ringfence of science research budget.

A statement on the group's website said the possibility of cuts would come as "a major disappointment to researchers across the country" who have already "weathered austere times".

Biologist and chair of Science is Vital, Dr Jennifer Rohn, said: "The government has talked about making Britain the best place in the world to do science. It needs to make good on that promise.

"In March we, together with over 50 renowned scientists, called for a long-term increase in science funding to 0.8% of GDP to ensure the future of science in the UK. BIS must find ways to meet its obligations to research by maintaining its promised funding in the short term, and in the long-term, by increasing it."