In a report from June 2018, All, Christopher Snowdon addressed the argument for “progressive regressivity” promoted by a number of advocates of food taxes. The report argues that the regressivity of such taxes are demonstrated empirically as they hit the poorest households disproportionately.
He then dimisses the argument that such taxes would benefit the poor the most, arguing that low-income groups continue to buy products that are taxed. He argues that even if they would benefit from health gains with such taxes, they would still suffer a net loss in their revenues.
Hence his conclusion is that advocates for food taxes should be honest about the fact that whatever their outcomes, food taxes will always be regressive.
The full report is available here.