With the childhood obesity strategy seemingly on hold until party conference season at least, there has been much frantic activity among the health lobby this week in an attempt to win the ear of new PM Theresa May.

Consumer group Which? ploughed in today. It re-ignited the debate over the promotion of so-called junk food in supermarkets, with new research claiming the majority of food and drink on offer on shelves is unhealthy.

It urged supermarkets and the government to agree on action to reverse the trend. In doing so, it returned to what was the number one call from PHE in its recommendations on sugar reduction, made to ministers last year.

But as the new-look government decides what to do next with its much-delayed strategy, retailers have made it clear this is a battleground that would make the sugar tax look like a relative walk in the park. If the new PM has done her research, she will know several previous attempts under the failed Responsibility Deal to tackle the thorny issue of promotions fell flat.

If the government wants to act on Which? and PHE’s call, it would need to go nuclear and legislate across categories covering hundreds if not thousands of products, somehow deciding what is and what is not ‘healthy’ – though, of course, in many cases this is far from black and white.

With the prospect of legal challenges from suppliers meaning each sector could take years to implement, even if such moves successfully negotiated competition rules, this is surely a battle the government can ill afford.

It’s not just an economic argument, either.

While some practices in the industry may be hard to defend, on this there is a strong counter-argument from retailers and suppliers, who argue it has never been cheaper to buy healthy food.

“I was actually pretty surprised at how much health food was on promotion,“ says one supplier source. The Which? study reckons it is 47% compared with 53% unhealthy. “Even with its dubious methodology, which would count things like nuts, cheese and oily fish as unhealthy, that’s still a massive load of products that are healthy being promoted every day,” the source adds.

In fact, Which? found that from April to June this year, no fewer than 36,000 promotions were on healthy food.

Yet that only tells half the story. While suppliers still rely heavily on promotions on price in a fiercely competitive landscape, regardless of whether they fall into the ‘healthy’ or ‘unhealthy’ camp, the fact is retailers have been increasingly moving away from promotions towards everyday low prices, driven not by intervention in the market but by competition with the discounters. This has seen the price of healthy products like fruit & veg plummet.

Sainsbury’s today hit back at Which?, saying it had introduced lower regular prices on thousands of its products including fresh produce last year, which had made them “affordable all the time”.

It also axed multibuy offers in its stores in June, and removed confectionery from its meal deal offer. Many others have taken similar action.

In Tesco’s case, as far as kids are concerned, fruit couldn’t be cheaper than it is now – it is literally giving the stuff away. Tesco tells The Grocer it expects to give one million pieces of fruit to children – per month, that is – in its open-ended initiative, which was rolled out last week.

If it was giving away free chocolate bars the campaigners would have more of a case (the kids might be happier, too). As it is, the call from Which? seems both impractical and unnecessary, seeing as market forces are doing the job for them.

Some would also argue the group has picked on the wrong target. Supermarkets may have thousands of promotions of so-called unhealthy food, alongside the thousands they have on healthy ones, but they provide the sort of choice consumers will not find in the row after row of kebab shops, burger bars and fried chicken takeaways often found up the road.

One wonders what the ratio of promotions skewed towards healthy products would be among them.