Brumwell, who is the general secretary of UCATT and chairman of the CSCS, wants the audit office to look at how many people working on government projects have cards. He also wants the NAO to consider whether migrant workers should be issued with them as part of the registration process.
The call comes as David Blunkett, the home secretary, outlined plans to issue migrant workers with work permits. The scheme is an attempt to regulate the expected influx of workers from the 10 countries that are joining the European Union on 1 May.
Writing in Building, Brumwell says the government should insist on CSCS registration for migrant workers to ensure standards are maintained.
He said: "The government and leading clients have an important role to play in securing a level playing field for the industry. They must insist on CSCS registration for all workers, including migrants."
Under the European accession programme, workers from Poland, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Slovakia and Slovenia will be free to work in the UK on certain conditions.
Other EU citizens, including those from Malta and Cyprus, who also join on 1 May, have an unconditional right to travel and live anywhere in the union. However, workers from these eight nations will have to apply for a work permit after they arrive in the UK, and they will face restrictions on their access to benefits if they decide to settle.
Sixty per cent of contractors report that they have difficulty finding staff
Blunkett outlined his plans to have a managed migration programme to parliament on Wednesday. He said: "We welcome people to come to our country to work to contribute and be part of our society. We reject those who come to exploit our hospitality."
The Home Office will extend the registration scheme to East European workers who are already living here illicitly and working in the black economy.
The Construction Confederation welcomed Blunkett's policy as an opportunity to solve contractors' skills shortages. A recent survey found that 60% of contractors reported difficulties in recruitment.
The Scottish economy is particularly hard hit by labour shortages. Syd Patton, the chief executive of Scottish Building, said Scotland needed skilled workers to carry out the large volumes of housing repair and maintenance.
Patton urged the government and the industry to make the CSCS the universally recognised benchmark. He said: "The first thing to ask is to get a CSCS card as minimum. It's entirely wrong of us not to insist on this being the minimum level before starting work in the industry."
Paul Corby, national construction officer at M&E union Amicus, attacked the government's plans as an attempt to keep down wages.