Those who apply to study arts-based subjects will still lose out this autumn, the National Union of Students (NUS) said.
Business Secretary Lord Mandelson today confirmed the Government would fund financial support for 10,000 extra students, including grants and tuition fee loans, but universities will get no extra money for teaching.
The emergency plans were announced to alleviate the crisis in university places for this September, amid fears almost 50,000 would-be students could miss out.
Lord Mandelson said the additional places would only be for full-time undergraduate entrants to science, technology, engineering and maths (Stem) subjects, as they would give young people the skills they needed for the "jobs of the future".
Aaron Porter, NUS vice-president of higher education, said they were pleased the Government had listened to concerns.
But he added: "Thousands of people who have applied to study non-Stem subjects are still going to be without a place in the summer.
"We understand the current pressures on public finances, but the Government must also make the right long-term decisions. It is surely better to bear the cost of additional university places now than to shoulder the burden of long-term unemployment later."
Lord Mandelson said: "By making available 10,000 extra places in science, technology and maths, we are not only helping more individuals with the ambition and ability to go to university but also investing in this country's future," he said.
Concerns were also raised that institutions would struggle to cope with the extra students without additional funding.
Phil Willis, chairman of the Commons select committee covering higher education, said the extra places were welcome.
"I do have concerns that the additional places will not be matched by extra teaching grants to universities," he added.
"Universities are struggling to meet the current demands and courses in science subjects tend to be more expensive than those in other subjects."
Professor Paul Wellings, vice-chancellor of Lancaster university and chairman-elect of the 1994 Group, which represents research-intensive universities, said: "1994 Group universities want to help meet this demand but additional teaching funding is also required to maintain the quality of student experience."
Dr Wendy Piatt, director-general of the Russell Group of leading universities, added her support.
She said: "The Russell Group also welcomes the fact that recruitment to Stem subjects this summer will no longer lead to penalty fines.
"However, any growth in the number of students must be funded in a sustainable way that will not create real and long-term difficulties for UK universities and undermine the quality of the student experience."
The costs of supporting the extra students will be met be "reprioritising" existing budgets, Lord Mandelson said.
And graduates will only have an optional two years' holiday on repaying student loans in future instead of five.
Diana Warwick, chief executive of Universities UK, which represents vice-chancellors, said: "We understand the thinking behind tying the student support to the Stem agenda at the current time; however, we would be concerned if this were, in future, to have a negative impact on areas such as the social sciences, arts and humanities."
Applications to UK universities are up almost 10 per cent this year - a surge in demand fuelled by the recession.
The Government previously capped student numbers, with just 3,000 extra places available for full-time first year students this year, because of a £200 million funding shortfall.
Sally Hunt, general secretary of the University and College Union (UCU), welcomed the Government's announcement, but said students cannot be "crammed" into universities if staff jobs are being cut.
"Our message to the Government is quite simple - if we want to ensure we are delivering the highest possible quality of education to our students, we have to abolish any notion that it can be done on the cheap.
"Who is going to teach the extra students if university jobs are being axed? Proper funding is required for the extra places and unnecessary job cuts must be stopped."
Liberal Democrat universities spokesman Stephen Williams said: "Universities will struggle to take on these extra students without being given the money they need for teaching."
Shadow universities minister David Willetts said: "The new places come with no funding for teaching - yet Stem courses cost more. Around 40,000 more applicants are likely to be rejected this year than last. And there is nothing for those whose A-Levels stop them from applying for Stem courses. We still face a summer crisis."
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