Travellers at some UK airports are receiving less than $1 for every £1 they change after a week of Brexit turmoil pushed sterling to fresh lows.

At Cardiff airport, the bureau de change was offering customers only $0.97 for every £1 on Friday. At Bristol airport, Moneycorp is giving customers only $1.03 for £1, while at Gatwick the rate is only $1.06. At Heathrow, Travelex is paying $1.05 for every £1.

British visitors to EU countries are also suffering a collapse in their buying power, with some airport exchange bureaux offering as little as €0.90 for every £1 this week.

Significantly better rates are available online and by pre-booking but for last-minute travellers changing their money at the airport, trips to the US have become very expensive.

This week the pound sagged below $1.25 on money markets compared to the $1.28-$1.30 range it was trading at before the latest bout of Brexit uncertainty. Before the June 2016 EU referendum, the pound had risen as high as $1.50, while in March 2008 it was briefly worth more than $2.00.

British tourists visiting New York at Christmas face eye-watering prices. Fancy a spin around the famous ice rink at Rockefeller Plaza? That’ll be £45.50 each, assuming the tourist only obtains $1 for every £1 at the airport. London’s equivalent, the rink at Somerset House, costs £11, plus a £2.95 booking fee.

Entry into New York’s top museums, such as the Guggenheim or Moma, will be £25 a head (again, assuming the visitor has only managed to obtain $1 for every £1), while Americans visiting London enjoy free entry into the Tate or the V&A.

Suzanne Bearne, a British journalist and Guardian Masterclass host, is just back from a stint of a couple of months in New York. She said: “The cost of living in New York is now crazy. I stayed in New York for a few months five years ago and it was much more liveable then. Now prices have shot up. A meal in a restaurant would be twice as much as back in London. Everything was two to three times as much as in the UK once tips and taxes were thrown on. I love New York to pieces but this time it’s star had waned – it ain’t as fun when you’re paying $20 for a drink and you have to keep an eye on your money so much.”

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Tourists wanting to catch a top show on Broadway will be stunned by the prices. The Book of Mormon is charging $836 to $998 for two seats in the stalls in New York on its official site. So British visitors suffering from a poor exchange rate could be paying the equivalent of nearly £1,000. The same show in London, on the same night in December, and on the same official site, will charge £184 to £404 for seats in the stalls. A New Yorker could almost fly to London and see the show for the same price as taking the subway to 49th Street and watching it there.

However, sterling’s plunge has turned London into a hot destination for US shoppers. The official government agency VisitBritain said flight bookings from the US to the UK “are showing a double-digit increase during the Christmas and new year period when compared to the same period last year”, while bookings for the first half of 2019 have jumped by 28%.

US visitors are the most valuable tourists to the UK in terms of spending. Although 2018 figures are not yet available, Americans spent a record £3.6bn visiting the UK during 2017, up nearly a 10th from before the referendum-induced fall in sterling.