A Whitehall source said McTaggart had agreed to meet Brumwell after he wrote to home secretary David Blunkett last year about the use of foreign workers in the building of the Home Office's new headquarters.
The source said: "Now that Brumwell is CSCS chairman, he is particularly keen to ensure that the foreign workers are properly accredited and being treated fairly on government projects."
Brumwell said that his next step was to galvanise the support of all government offices that procure construction. He said: "I will be making it my first priority to meet with these departments to encourage them to promote CSCS among their contractors."
He added that CSCS was already an identifiable standard for the industry, and it was his aim to further promote the CSCS brand.
Brumwell is particularly keen to ensure that the foreign workers are properly accredited and being treated fairly
Outgoing CSCS chairman Tony Merricks stood down after serving 10 years in the post, during which time he successfully united the industry behind a single competency-based scheme and raised its membership to almost 600,000.