Zaffar was a passionate campaigner on environmental issues, founded the Clean Air Justice Network and called for pollution levels to be brought down across the city.
He was also often the one answering questions as the city council brought in the Clean Air Zone in 2021.
Writing on Facebook, Councillor Saima Ahmed said Zaffar was always ready to offer help and support.
She added that he “believed deeply in equality ” and “consistently spoke up for the community and his colleagues regardless of political differences”.
“His loss is felt deeply – the community, his friends and all of us who had the honour of knowing him. We have lost a leader, a voice of integrity and a kind-hearted friend.”
He was a member of the Sustainability and Transport, and Neighbourhoods scrutiny committees, and most recently was part of the Safety Advisory Group that came under fire for the decision to ban Maccabi Tel Aviv fans from Villa Park.
Key cabinet posts he held over the years also included transport, equalities and social justice, although he stepped down as equalities chief in 2017 after criticism from the government integration tsar.
Conservative group leader Robert Alden said while he and Zaffar held very different views on many matters, he “clearly cared deeply for his local community”.
“It’s awful to hear this news and our thoughts and prayers are with his family and friends at this horrendous time,” he said.