He died on Tuesday morning after contracting an infection following a minor operation 10 days ago.
Mr Brumwell became a full-time union official at Doncaster Racecourse in 1969. He rose to become general secretary in 1991 and led Ucatt from the union's financial and political turbulence of the early 1990s to stability.
He sat as a commissioner on the Health and Safety Commission from 1998 and chaired Constructing Better Health, the occupational health pilot scheme.
He also led the campaign to qualify the construction workforce as chairman of the CSCS scheme for two years.
Three years ago he brokered a groundbreaking pay deal for workers on Heathrow's Terminal 5 project with Laing O'Rourke and client BAA.
TGWU construction secretary Bob Blackman said: 'George was a good friend and an industry champion who fought tirelessly to gain recognition for the contribution construction workers make to society. It's a tragedy.'
Construction Confederation chief executive Stephen Ratcliffe said: 'He had a distinguished career and continued to make a significant contribution. He will be sorely missed both as a friend and a colleague.'
Mr Brumwell gained a CBE in 2003 for his services to construction.