Philip Hammond, under pressure to ease austerity, must spend the summer preparing the ground for sweeping tax rises that catch everyone in their net.

A tax on the rich is not going to be enough to meet the demand for £20bn extra on health spending by the end of the parliament, let alone the cost of extra police officers to tackle a significant rise in crime, higher social care funding and a boost to the defence budget.

Whether you focus on the richest 1% or even the best-paid 10%, the exchequer needs more cash than high earners can supply: that seems to be the thinking inside the Treasury. All households must pay something towards these necessary budget increases.

It won’t be revealed until the autumn budget what taxes Hammond thinks we should pay more of. His plan could be a shock-horror rise in the standard 20p rate of income tax or a higher rate on national insurance. Then again, he may prefer taking aim at consumption taxes like VAT and fuel duty.

The chancellor has already tapped extra revenues from stealth taxes – the little-known surcharges that became widely used during Gordon Brown’s reign at No 11. We are all paying higher insurance premiums thanks to sharp increases in insurance premium tax in the last two years. This revenue stream helped the public finances. Yet it was just a drop in the ocean.

After eight years of austerity there are holes in public services that need filling and it will take big money to do it. Likewise, welfare benefits are crying out for a cash injection, if only to keep pace with inflation.

A boost to health spending has already been singled out by the Treasury’s official economic forecaster, the Office for Budget Responsibility (OBR), as an unfunded commitment that will upend current budget projections.

Almost every department has its hand out begging for more funding, and all with legitimate claims. James Brokenshire, the housing and communities secretary, must go to bed at night relieved that all 418 councils he oversees met their statutory duties that day, especially those concerned with keeping children safe. Most local authority finance directors believe that the day is nearing when government cuts eat into their ability to deliver the most basic of services.

Another area desperately short of funds is social care. The OBR chairman, Robert Chote, said last week that should the government agree on a deal over social care funding, it would cost the health department more money than it currently spends. This must be true when most older people pay for their own care and a deal would cap that amount, leaving the state to pick up the rest of the cost.

Universal credit is another claim on the pubic purse. This week the Resolution Foundation will illustrate the power of the credit to raise incomes and reduce child poverty. This government has severely cut tax credits since 2012 in the hope that wage rises would fill the vacuum. They haven’t, harming family incomes and pushing up child poverty.

It would take many billions of pounds to reverse this trend, just as it would take tens of billions to inject enough funds to maintain public services over the coming years, let alone improve them.

Hammond seems optimistic that Brexit tensions will allow him to throw away the Tory manifesto ban on mainstream tax rises. Photograph: Wiktor Szymanowicz/Barcroft Images

There are different routes out of this mess. The UK government can continue selling off assets to foreign buyers, much as Premier League football clubs do to raise funds.

There are private schools selling parts of themselves to the Chinese to fund expensive developments. Maybe state schools will follow? Universities are increasingly in hock to foreign sponsors. It might not be long before one of the top-ranked institutions adds the word Emirates to its name.

Hospital trusts are in the midst of a fire sale of land expected to bring in several billion pounds. Network Rail is preparing to sell all the commercial space under its arches to get the cash today rather than the rental income in perpetuity.

Alternatively, the state can borrow. There are local authorities raising bonds to keep themselves afloat. And the government itself could borrow more, especially as the chancellor is on target to reduce the annual spending deficit to below his target of 2% in this financial year.

Hammond seems optimistic that amid the tense and possibly chaotic votes expected in October over Brexit, he will be allowed to throw away the Tory manifesto and its ban on mainstream tax rises. Jacob Rees-Mogg, the architect last year of a rebellion over a £1.2bn national insurance rise on the self-employed, will be too distracted to care, goes the thinking.

It seems far-fetched, to say the least. Which leaves the UK selling its assets and using its borrowing power to make ends meet.