The combined account, which was previously held by Publicis, comprises the Kingsmill and Allinson brands, along with the Burgen and Sunblest ranges.
JWT picked up the business in a head-to-head pitch against Publicis after Clemmow Hornby Inge and Delaney Lund Knox Warren & Partners were knocked out at an earlier stage. The review process was overseen by the Yardley Creer Partnership.
Ros King, the JWT managing director, said: "Kingsmill is a great British brand that we are delighted to be working with. We came up with a simple strategic solution and then took a massive creative leap.
"Allied Bakeries is a fantastic client who has bought into a campaign that I am sure will be talked about."
Kingsmill, the UK's sixth-biggest grocery brand, uses the TV presenters Mel Giedroyc and Sue Perkins to front its communications. But it recently signed the sports presenter Gabby Logan to front its "kit for clubs" initiative - a scheme where customers collect tokens and exchange them for free sports equipment for adult sports clubs.
Jo Sykes, the Allied Bakeries marketing director, said: "JWT's plans for our portfolio were extremely strong and it has challenged our traditional way of thinking."
Allied Bakeries' media account, held by ZenithOptimedia UK, is unaffected.