The push, launched earlier this month, will be highlighted at the association's conference and trade show on 19 January.
Chairman Phillip Effingham said: "One of the real focuses of the event will be the campaign. Over recent years we have seen a reduction in acreage of brassicas. Cauliflower has been one of the biggest casualties, falling around 20% over three years."
The campaign will target press, TV and radio and flag up the health benefits of crops and highlight that they are home grown, he said.
"It will be a drip-drip process rather than a push on point of sale and the shelves, where the message is soon forgotten. We hope to win over the hearts and minds of consumers over a period of time."
Other speakers at the show in Lincoln will talk on club root, weed and pest control, the recession and ensuring profitable markets for Brassicas.
Effingham said good weather had ensured "exceptionally good" demand for sprouts, strong yields and low wastage. But prices were "average".
He added: "Releasing more sprouts into the market is depressing prices. The world and his dog have had ample quantities of produce and this has impacted on profitability in the Brassica sector."
For conference details, call the BGA on 01507 602427.