The arrival of Theresa May in Downing Street was heralded as the beginning of a more interventionist age. Unlike her predecessor, May would act decisively to correct market failure and protect the public interest.

But the new prime minister is so far proving to be a selective interventionist. Having promised a stricter approach to foreign takeovers, she nevertheless approved the planned £24.3bn purchase of ARM Holdings, the UK's largest technology firm, by Japan's SoftBank. The government argued that the deal represented value for money. But Tory free marketers suggested it proved that the post-Brexit need for foreign investment will trump more protectionist instincts.

May has now infuriated public health campaigners by diluting the government's anti-obesity strategy. Though the "sugar levy" announced by George Osborne in his final Budget has been retained, proposed restrictions on junk food advertising and promotional deals have been excised. Campaigners argue that May has put the interests of business before those of the nation's children (a third of whom are overweight or obese when they leave primary school). Sarah Wollaston, the Conservative chair of the health select committee, said: "Watered-down strategy is at odds with the pledge to tackle the 'burning injustice' of health inequality." But other Tories are welcoming the announcement as a signal that the advance of the "nanny state" has been halted.

If May holds true to her rhetoric, there is much interventionism to come. She has promised worker representation on company boards, binding shareholder votes on executive pay and Treasury-backed bonds. Such is her commitment to "industrial strategy" that the words have been included in the title of a remodelled business department.

But in two of the areas where Cameron proved most interventionist - climate change and international development - MPs anticipate less activity. The Department for Energy and Climate Change was abolished, viewed as evidence of her lesser commitment to environmentalism. May's joint chief of staff, Nick Timothy, perhaps her biggest intellectual influence, once referred to the climate change act as a "unilateral and monstrous act of self-harm" owing to its effect on energy prices.

The international development secretary, Priti Patel, called in 2013 for her department to be replaced with one more focused on trade. Her new special adviser, Robert Oxley, argued for the abolition of the 0.7 per cent aid spending target (which Cameron upheld in defiance of Tory MPs) while at the Taxpayers' Alliance in 2014 (though government sources emphasise that it is both "a legal commitment" and a "manifesto commitment).

Only when May seeks her own mandate at a general election while her policy direction be fully known. But rather than interventionism tout court, the early signs are that the state will advance in some areas while retreating in others. Like Cameron, May will act when she believes it matters. But, once again, their priorities have been shown to be sharply distinct.