Kenrick was appointed business director on Fallon's £70m Asda account in August, at the request of Asda chief marketing officer Rick Bendel.
Earlier this month, Asda moved its business into Fallon's sister agency Saatchi & Saatchi, while Fallon retained the £3.5m George clothing account.
Kenrick said she left Fallon prior to the loss of the Asda account and will not be joining Saatchi & Saatchi.
She had previously worked as Asda's head of regional marketing and marketing director for George. She is also a former Camelot marketing director.
Kenrick joined B&Q as marketing and customer proposition director in 2006, remaining there until last December.
She leads a partnership between The Marketing Society and Prince Charles' May Day Alliance aimed at clarifying environmental claims made in advertisements.
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