The pound has tumbled to a new seven-month low against the dollar and three-month low against the euro as fears mount that Brexit negotiations are going nowhere and household debt is too high.

Sterling fell 0.4 per cent to $1.3098 and 0.3 per cent to €1.1307 as European leaders convened for a key summit on Thursday and Friday.

Theresa May is due to brief her European counterparts on the progress made on Brexit at a dinner in Brussels – but for EU nations other than the UK, migration is a more pressing concern.

The meeting comes as a group of MPs warned the prime minister that an amendment may be needed to Article 50 in order to prevent the UK crashing out of the EU without a trade deal, an outcome that could be disastrous for a host of sectors.

Irish Taoiseach Leo Varadkar said the lack of progress on negotiations was “very disappointing”.

“Time is running out for the withdrawal agreement to be concluded satisfactorily by the October council,” he said ahead of the summit.

Also weighing on sterling were comments from Bank of England deputy governor Jon Cunliffe, which appeared to play down talk of a sharp rise in interest rates.

Mr Cunliffe, one of six members of the BoE’s Monetary Policy Committee (MPC) to vote to keep rates at 0.5 per cent last week, said: “Financial markets are assuming that interest rates go up by another three-quarters of a percentage point over the next couple of years.

“We do our forecasting on the basis of where the financial markets have those interest rates, and we think we have inflation at target at those sorts of levels.”

The Bank issued a warning on Wednesday that high levels of household debt pose a risk to financial stability. Mr Cunliffe said indebted families could be in trouble if the economy goes into a recession.

Connor Campbell, a financial analyst at Spreadex, described the pound’s performance as “utterly miserable”.