Boris Johnson barely has a plan for the economy now – what will he do when no deal pushes us into a recession?

No sooner has Boris Johnson returned to Downing Street from his UK sunshine tour than the chief-gloomster-and-doomster himself, Mark Carney, governor of the Bank of England, rained all over the prime ministerial parade.

Thankfully the UK still has an independent Bank of England and an independent-minded governor who is willing to spell out to ministers and public alike some unpalatable truths about the no-deal Brexit we may now be moving towards. Mr Carney was careful to stress, as he should, that government policy is still to secure a deal, and thus a transition period; but that the possibility of no deal has been there since the day after the referendum and remains there now.

Even in the case of a smooth Brexit, with a deal and a transition period, the governor sees a one-in-three chance of a recession. With a no-deal Brexit, that likelihood would rise and, in any case, a no-deal Brexit, like any other Brexit scenario, would mean lower growth and higher inflation than would otherwise be the case. It is as simple as that.

Most worryingly, there would be a sharp slowdown in business investment, which will have damaging long-term effects on expanding the productive potential of the British economy – productivity, wages and living standards will be depressed compared with the alternative of staying in the EU for many years to come. The Bank of England will “support” jobs and activity, but it will also need action from the government.

What then to make of Mr Johnson’s recent, almost casual promises to increase public spending? Will they, as he claims, be the “rocket boosters” the nation will need?

In order to be so they would need to be even more substantial than they are now. The more certain of the pledges – none has yet been formalised over any given period of time – is a boost to the police, to schools funding, to no-deal preparations and a fund for “left behind” northern towns, presumably as a part of the revived Northern Powerhouse. It might amount to roughly £10bn a year. That is about a third of the £26bn “fiscal headroom” bequeathed to the Johnson administration by the prudence of the last chancellor, Philip Hammond. That would leave some more billions for tax cuts and other schemes to mitigate the worst effects of a no-deal Brexit.

Even on some optimistic assumptions about the multiplier effects of such an injection, and on confidence and economic activity generally, that £26bn simply cannot replace the withdrawal of private sector investment and spending. Nor would any conceivable monetary easing by the Bank of England. The Public Accounts Committee of the House of Commons has cast doubt on how rapidly the economy can absorb such huge fiscal stimulus, and in particular how effectively the billions devoted to no-deal Brexit can be expended.

There are other problems with these sketchy fiscal plans. They would increase borrowing, but not all of them qualify for the golden rule of borrowing to fund infrastructure investment. In particular, tax cuts for the wealthy – if Mr Johnson and his new chancellor Sajid Javid feel emboldened to unveil a “Global Britain enterprise budget” in the autumn – would most likely be saved and invested abroad.

If the no-deal Brexit slowdown proves more severe than thought, and if the world economy slows down even more rapidly than feared, then borrowing will also rise – assuming that the government will allow the usual “automatic stabilisers” to operate, and accommodate the increase in public spending on benefits and a fall in tax receipts.

There are also some critical questions about how the government is planning to boost education spending in particular.

Conservative backbenchers representing shire constituencies have long lobbied for an increase in their funding-per-pupil, which has fallen behind schools in more deprived urban districts – deliberately so in order to address intractable problems in state schools in poorer areas. This is what the Con-Lib Dem coalition achieved with the “pupil premium”. Now it is to be diluted.

Mr Johnson’s scheme, predictably, is to make sure there are no losers, in absolute terms, and “level up” the spending – but that is intrinsically unfair.

Much of the money will still be targeted at pupils who have a relative educational advantage in reality. Schools with more affluent intakes – including more than nine in 10 grammar schools – will benefit under the proposal, and the initiative comes at a time when progress in closing the attainment gap has stalled and is at risk of going into reverse.

In the longer run, if the impact of Brexit on the economic health of the nation is anything like the predictions, then there will in any case be less available for the whole universe of public spending, and the choices will be about where to make the cuts. There will be few, if any, winners under any variety of Brexit.