The union was responding to today's House of Lords Science and Technology Committee report on 'Higher education in STEM subjects'.
Prospect head of research Sue Ferns said the union supported the committee's findings that STEM students face a triple whammy of higher fees, lack of student finance and the decline in the number of overseas students.
Ferns welcomed the proposal to set up an expert group to consider the supply and demand of STEM postgraduate provision in the UK, involving employers.
But she said: "Alongside attracting new entrants, access routes need to be opened up to people who already have high-level STEM skills. For example, the government must address under-representation of women and black and ethnic minority groups in some STEM disciplines, something that this report does not address. For this reason, the expert group should also include representation from employees as well as employers.
"We also welcome the call for a single body to provide real-time data analysis and a commentary of where STEM shortages exist. Such a body must have Cabinet-level cross-government authority in order to make a difference. Prospect has been calling for this for many years in the light of the fact that the government does not even know how many scientists or engineers it employs, or their areas of expertise."
Ferns said the current climate of cost-driven closures, cuts and privatisations would not help to attract a new generation of scientists. "If the government wants to maintain the UK's SET capacity then it has to put its own house in order.
"Actions such as closing down the Forensic Science Service, denuding the Ministry of Defence of civilian expertise and decimating the resources of Forest Research do not help. Seeing thousands of specialists losing their jobs does not send out the right message to future generations of potential scientists. Yet science, research and innovation are vital to the UK's economic growth."
Prospect represents 80,000 members working for employers who carry out science, engineering or technology functions.