A memorial event was held on Friday after his death at his home in Chippenham, Wiltshire.
Having severed his link with the agency in 2014, two years after its sale to Publicis Groupe, Shaw was the chief executive of a consultancy that worked with agencies to provide business advice, mentoring, coaching and training.
After his cancer diagnosis in the spring of last year, he blogged under the name of Mr Kidlung about his life while undergoing treatment, writing his last blog little more than a month before his death.
Marc Nohr, his former business partner, said: "Where other people would have just given up Jeremy wrote very eloquently about what was happening to him."
With a direct marketing career that spanned three decades, Shaw built a reputation as a shrewd behind-the-scenes manager. He once told his partners: "You concentrate on building the profile – I’ll keep the trains running on time."
A Cambridge graduate, he began his career in the charity sector with Oxfam and Barnardo’s before joining Smith Bundy & Partners as managing director in 1984.
After 13 years at the agency, latterly as chairman, he spent a year at Carlson before his hiring by 141, the Bates-owned below-the-line unit. He saw it through a tumultuous period that dogged its transformation into a fully integrated agency, a process that provoked a string of senior resignations.
It was his stint at 141 that brought him into contact with Paul Kitcatt, then the executive creative director. They quit the agency together in September 2000 subsequently linking with Nohr and Vonnie Alexander to launch Kitcatt Nohr Alexander Shaw in 2002 with investment company backing.
Away from the agency, Shaw was heavily involved with IPA initiatives on diversity – of which he was a passionate advocate – and continuous professional development.
After taking time out for go sailing for a year, he returned to assume the duties of chief operating officer before taking the title formerly at its Publicis sister agency, Digitas. He and Nohr quit in late 2014 to be followed soon afterwards by Kitcatt and Alexander.
Nohr said: "Jeremy wasn’t only a good businessman but a real grown-up who always offered a balanced opinion. He was a man of quick intellect and utter integrity and was always there for other people."
Shaw is survived by his wife, son and daughter.