Scottish families stand to lose hundreds of millions of pounds over the next few years from a combination of rising inflation and a freeze on welfare payments like child benefit.

More than a million Scottish families will see their income fall by £360 a year by 2020, experts predict.

The Institute for Fiscal Studies (IFS) think tank accused Conservative ministers of passing the risk of an inflation hike onto millions of ordinary working families and warned it would lead to lower living standards.

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The IFS estimates that 11.5 million working families across the UK will lose an average of £260 a year because of the decision to freeze most social security payments in cash terms.

But once new inflation forecasts are factored in, that figure rises to £360 a year.

At the same time the freeze is predicted to save ministers around £4 billion a year, £1bn more than expected.

The warning came as it was announced that inflation has hit its highest rate for almost two years.

The peak led to fears of a substantial rise in the cost of living in the wake of the shock Brexit vote.

The IFS said that normally benefit and tax credit rates increased each April in line with the previous September's inflation rate, meaning that ‘higher prices lead to higher benefit rates’.

However, it said, last year the then Chancellor, George Osborne, announced plans to cut social security spending by £12 billion that saw most working-age payments frozen in real terms until March 2020.

The IFS said the policy “represented a significant takeaway from a large number of working age households”.

But it also saw the “risk” of inflation pass from ministers to benefit recipients.

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"While it is perfectly reasonable to argue - as the 2015 Conservative Party manifesto did - that the working-age benefit system should be made less generous over this parliament, it is hard to see why the appropriate size of cut should be arbitrarily determined by the impact of movements in sterling on prices, " the IFS said.

Liberal Democrat Treasury spokeswoman Susan Kramer said: “The decision to unnecessarily continue to freeze benefits was already a deeply damaging, but now the Government’s making things even worse thanks to their reckless actions over hard Brexit - putting even more pain on low income families.

“It’s time that the Government accepted that unfreezing benefits is not only morally necessary, but also important in injecting vital resources into the economy through spending by those on lower incomes.”

The row came as it was announced that the Consumer Prices Index had reached one per cent for the first time since November 2014, much higher than the previously forecast 0.6 per cent.

Some economists have predicted that it could reach as high as 3 per cent by next year, a rate that would far outstrip average wage rises.

Since the referendum result the value of the pound has fallen from almost $1.50 to around $1.20.

Experts warn the drop will lead to increases in the price of imported goods.

Last week Tesco stores across the UK ran out of products like Marmite after the supermarket refused to pay a higher price to the manufacturer.

Benefits that have been frozen include Job Seeker's Allowance, Employment and Support Allowance, some types of Housing Benefit, and Child Benefit.

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Pensions, Maternity Pay and disability benefits are excluded.

Michael Martins, from the Institute of Directors, said that much of the inflation rise could be traced to the fall in the pound caused by the referendum result, and more recently, Theresa May’s announcement that Brexit negotiations would begin next year.

And he warned that the UK could even suffer from "stagflation" where the economy shrinks at the same time as inflation rises.

“Prices will likely continue to rise," he warned. "Given weak wage growth in recent years, it seems likely that higher inflation, especially on essential items like food and energy, will begin to eat into real disposable income. We are seeing some signs of belt-tightening in big ticket items like furniture already.

“If wages and business investment enter a serious decline, the UK could find itself along the path towards stagflation, where an economy stalls or shrinks, but inflation increases – a particularly nasty spiral.”

Matt Whittaker, chief economist at the Resolution Foundation, said the latest figures suggested that the "historically low inflation that has supported living standards over the last two years may not last much longer."

He warned that unless more of the population got a press rise their standard of living would fall.

He said: “We’re unlikely to see the full effect of the fall in sterling on day-to-day prices until 2017 but, even though inflation remains well below target for the moment, Britain’s pay recovery already appears to be faltering.

“If pay settlements don’t rise significantly we will see a fresh wage squeeze next year.”