The Tories’ audacious election gamble may have paid off with the acquiring of several new, formerly rock-solid Labour seats in the north of England; for the voters of these so called “left-behind” towns, however, the dice is still rolling. They staked their votes on Brexit getting “done” and a renewal of their local economies and public services. The prime minister has promised investment in new rail projects and the NHS to reward that trust. But can he be trusted to deliver?

Boris Johnson humbly thanked northern voters last week for “loaning” him those votes, but he may decide a five-year loan is all he needs to enact the wider economic and societal changes he desires. As we know, his word is not his bond, and erstwhile friends are ruthlessly dispensed with when no longer useful. Amid the triumphalism, Ben Bradley, Tory MP for Mansfield, signalled a note of caution: “We may be saying the right things but we are not trusted. The proof will be in the delivery; in showing whose side we are on.”

The Conservatives have shown minimal political interest in the 50 most deprived constituencies of England; it now represents 10 of them

Even if Johnson intends to keep his promises, how will he show whose side he is on? Grand multibillion-pound capital infrastructure projects are undoubtedly needed in the north of England. But they take years to implement. There remains – and not just in the north of England – the messy, human, day-to-day crises of poverty, social care and universal credit; collapsing local government; unaffordable housing; pitiful public transport, financially stressed schools and spiralling homelessness. There is little to suggest so far that, on these, the new government has the capacity, imagination or desire to offer anything new.

Delivery is hard for governments at the best of times. It is arguably easier when ministers are fulfilling long-cherished plans. Record NHS investment under Labour, for example, or rolling out Sure Start, felt like the natural reflex of a government largely in agreement about what to do, not a pragmatic obligation. In contrast, focusing the energies of the state on the neglected Midlands and north will not come easy to a Tory party that has spent much of its time in power over many decades doing the opposite.

Every new Tory leader declares themselves to be of the “one-nation” variety. The truth is that in recent years they have made an art form of ensuring austerity cuts fell far harder in the deprived north, and in Labour-voting cities, than they did in their south-eastern heartlands. The government is carrying out a so-called “fair funding” review of local government grants that – by watering down the significance of deprivation in the grant distribution formula – potentially has the effect of diverting cash from “red wall” metropolitan boroughs to the Tory shires. It was a policy dreamed up when Tories had minimal political interest in the 50 most deprived constituencies of England; it now represents 10 of them.

Boris Johnson announces plans for spending spree in north Read more

These policies are the product of the ingrained small-state, free-market, southern-centric instincts of a generation of Tory politicians still very much in the driving seat. Will Tory MPs in Redcar, Sedgefield and the rest, really change anything for the better? We shouldn’t be surprised if they don’t.

• Patrick Butler is the Guardian’s social policy editor