The NGA merged with the Society of Graphical and Allied Trades in 1990. Dubbins won the subsequent election against Brenda Dean, SOGAT's General Secretary, to become the first, and only, general secretary of the Graphical, Paper and Media Union.
He was president of the Trades Union Congress in 1997.
Between 2003 and 2008 he was chairman of the Trade Union and Labour Party Liaison Organisation. During this period he delivered the groundbreaking Warwick Agreement, ensuring every employee was entitled to 20 days paid holiday and maternity leave was increased to nine months. He led the campaign to ensure employment rights for Agency and Temporary Workers.
Dubbins is a keen West Ham United supporter.