Tax it instead. Enough tax to reduce consumption and make healthier food more competitive. But not so much that a large black market takes off.
It doesn't work for addictive substancies (like sugar), people will just pay more. We have sugar tax in Poland already and it didn't change anything. We also have 105% tax on cigarettes, yet still a lot of people smoke.
Again: the smoking and sugar consumption rate have both been declining in your country.[1][2]