In a statement, the BII said he passed away suddenly in his sleep at home on Sunday.
"The thoughts of the whole team at the BII are with his family at this incredibly sad time," the organisation said.
Tim Hulme, BII chief executive, said: "We are all deeply shocked at this sad news and all our thoughts are with Bernard’s family. He had played a pivotal role in the transformation the BII has been undergoing over the last year and was liked and respected by everyone who knew him.
"He will be missed greatly by all of us at the BII."
Leading trade figures and MPs were also quick to pay tribute.
A long-standing publican, Brindley was an active member of the BII for many years. He was the central region chairman of the organisation before becoming its overall chairman in 2012.
In recent years he had been a pivotal figure in the debate around self regulation in the tenanted pub sector.
He was heavily involved in schemes such as the Pub Independent Rent Review Service, which he chaired, and the Industry Framework Code for pub company codes of practices.