The agency won the business after a pitch against the incumbent agency, Mortimer Whittaker O'Sullivan.
M&C, which became an Allied Bakeries roster agency after landing the Kingsmill account last year, will begin work on the accounts in early 2008.
The company is planning heavy investment over the next two years as part of a relaunch of the bread brands.
Allinson was made famous in the 80s with its "bread wi' nowt taken out" line, while Burgen has recently gained popularity as a health brand for women.
Jon Wilson, the marketing director at Allied Bakeries, said: "We felt that the strategic rigour and creative spark the agency demonstrated on Kingsmill would be a fantastic asset for our Allinson and Burgen brands next year."