By the autumn we will find out how the Tories will make welfare cuts of £12bn a year by 2018. If they go ahead – and there are difficult political choices to be made here – these cuts will amount to one of the defining social policy decisions of the next five years.

The Tories were curiously loathe to explain how they would make these cuts during the election campaign. Either they knew, but were not telling because the truth would scare voters; or they didn’t know, but it didn’t matter because this was only ever a coalition bargaining chip to trade with the Lib Dems.

Ironically, a Conservative majority government may now find itself having to take unpopular choices it perhaps never really expected to have to make.

As we know from this week’s leaked Whitehall documents, when it comes to cuts there is no longer any “low-hanging fruit”. What’s left are in large part harsh cuts hitting middle-income working families: or, as the Institute for Fiscal Studies politely puts it, the “less palatable options”.

What we do know is that the Tories will freeze the level of working-age benefits for two years from next April, disqualify most 18- to 21-year-olds from claiming housing benefit, and reduce the household benefit cap from £26,000 to £23,000. Those three policies, the IFS calculates, will find the Tories about £1.5bn a year.

So where will the remaining £10.5bn come from?

The Tory line throughout the campaign has been: trust us on our track record. We made the cuts before, and we’ll make them again. The coalition did indeed make about £18bn of welfare cuts over the last parliament – but importantly, in view of what they need to achieve over the next five years, very little in the way of savings.

The bulk of the cuts – roughly two thirds – came from below-inflation uprating of benefits; the rest from restricting child benefit for wealthier families and some cuts to child tax credit. The cuts made here were more or less cancelled out by massive overspending on disability benefits and housing benefit.

According to social researcher Declan Gaffney, the net savings from five years of supposed welfare “revolution”, measured against the savings expected in 2010, were about £2bn. Contrary to Tory rhetoric, the coalition track record on finding welfare savings was dismal.

To reach £12bn by 2018, the Tories will not only have to massively increase the pace of welfare cuts made over the past five years, but achieve net savings. They will have to focus on the five big ticket items: tax credits (currently about £30bn a year); housing benefit (£21bn); disability living allowance and personal independence payments (£15bn); incapacity benefits (£14bn); and child benefit (£12bn).

One key area will be incapacity benefit spending. Previous attempts to cut this failed (spending rose at least £3bn above anticipated levels under the coalition): the high number of successful appeals against the notoriously unpopular fit-for-work tests revealed that there were simply not, as the coalition passionately believed, millions of people fraudulently claiming the benefit.

The Department for Work and Pensions believes there is scope for reform, however, and we can expect more drastic measures to try to reduce the numbers claiming employment and support allowance, by moving as many as possible on to the less-well remunerated jobseeker’s allowance.

This will be controversial, and Whitehall has concerns over the ability of the outsourced service (formerly run by Atos, now Maximus) to do this. Savings here will be painful, in human terms, and are far from guaranteed.

Housing benefit will be another target area, but the anticipated increase in spending (up £3bn a year from 2020) will be difficult to reverse given the growth in working households on low or static incomes forced to draw on housing support to meet high rents, particularly in London and the south.

Tax credits and child benefit cuts would appear to be necessary but they will take hundreds if not thousands of pounds a year out of the pockets of many of the middle-England voters that delivered David Cameron the premiership. Cuts to smaller budget items, such as carer’s allowance and statutory maternity pay may deliver marginal savings but at the cost of alienating the same demographic.

The Conservatives will look to a relatively buoyant employment market to reduce spending on unemployment benefit. But this relatively small budget line will do nothing to get them close to the £12bn target. Universal credit will be heralded as a technological fix to benefits spending by increasing the incentives for people on a range of in- and out-of-work benefits to come off the dole or work more hours. But the troubled programme is way off schedule (it may not be working fully until 2017 at the earliest) and there is no hard evidence it will deliver savings.

There will be much emphasis on so-called behavioural change policies, even though they will deliver barely any savings (and may not work even on their own terms). The benefit cap will continue, and there will be the threat of benefit sanctions for alcohol or drug addicted,​ mentally ill, or obese claimants who refuse treatment programmes.

The decision for​ the Tories is how many of these cuts they want to deliver and what the political costs of this will be. There is no coalition partner to blame if they don’t offer up £12bn; but if they take their foot off the welfare cuts pedal the imperatives of ​​deficit reduction mean savings will have to be found from other departmental budgets.

Cameron spoke this morning of a “one nation” Toryism but he will know his £12bn of cuts will disproportionately hit the poor, young sick and​ disabled. The cuts will deliver more pain, fear and instability to those they affect. We can expect a rise in child poverty, a further decline in living standards for all but the most well-off, and more stupendous rises in productivity in the food bank sector.

A majority gives the Tories a mandate to begin seriously dismantling the welfare state, but Cameron – if not all of his party – will know this carries a political cost. Deliver social security cuts on this scale and many of those who voted for him yesterday may be surprised to find that it is they, and not the mythical scroungers and shirkers of Tory demagoguery, who will lose out.