Jacques joined the firm as head of the Brussels office in 2000, later transferring to London.
A British national, he has spent the last couple of years in the firm's New York office, but left last month.
Clients have included cruise firm Carnival, tech firm Autonomy, the Barclay twins, Kraft Foods, Abbvie and TFI Tab Food Investments.
Prior to Brunswick, he had a career in the UK Government across the Foreign & Commonwealth Office, Cabinet Office and the Department of Trade and Industry (now BEIS).
His LinkedIn profile states: "Roles included leading on anti-trust and industry issues at the United Kingdom Permanent Representation to the European Union (UKREP), coordinating policy on European regulation at the Cabinet Office and negotiating bilateral trade issues between the UK and North America."
Brunswick declined to comment. It was not possible to reach Jacques.
In late 2017, Jacques also stepped away from his role as chair at cultural body the British Institute of Florence.