Dunmall joined Bauer Media at the end of 2013 from Naked Media where he was global chief executive. He was appointed as the group managing director of advertising in November 2013.
A spokeswoman for Bauer Media said: "Richard will be taking a break and exploring the next opportunity for his commercial talents."
The restructure comes as Bauer accelerates the integration of its content and commercial operations.
Abby Carvosso, the group managing director, will take on Dunmall's responsibilities, with a remit to build an "alignment" between commercial and content for advertisers.
Meanwhile, Rob Munro-Hall becomes the group managing director of magazine media, where he will take responsibility for all of Bauer Media UK’s lifestyle and specialist magazine media brands.
Sam Jones, the managing director of Bauer Xcel, the company's digital division, will extend his responsibilities across all of Bauer Media’s digital activities in the UK.
The restructure will also see the inclusion of the digital teams and activities from Bauer’s specialist publishing division, led by Charlie Calton-Watson.
Paul Keenan, the chief executive of Bauer Media UK, said: "The opportunities and challenges of today’s media market requires outstanding platform-specific skills, smart brand management, confident cross-platform and strong creative sales leadership.
"With the creation of this new Bauer Media UK leadership team, an outstanding management team launching new services to extend our radio business and the development of our new broadcast businesses in the Nordic markets we are well placed to realise the multiple opportunities such a dynamic market presents us with.
"I would like to thank Richard for his contribution to our commercial operation which has resulted in a new and sharper focus. He leaves with our best wishes for the future."