A new European Union regulation that came into force on 1 May is causing chaos among holidaymakers heading to Switzerland who hire a car.

The rule bans EU citizens from driving non-EU registered hire cars in the EU. But with Switzerland, a non-member, at the heart of Europe there are problems at car hire offices: a Swiss-registered hire car cannot be driven across the border to France, Germany, Italy or Austria by an EU citizen (such as a Briton). If the driver behind the wheel is Swiss, that it is permissible – as it is if the hirer has come from outside the EU. One company we contacted in Zurich called the change “completely ridiculous”. Some are having to stock French or German-registered cars; others are telling clients they can’t leave the country.

Guardian Money was first alerted to the issue by reader Jackie Greaney from West Molesey. When she arrived at the Alamo car rental desk at Zurich airport earlier this month, she was told she could not take the car she had booked across the border to Germany: “Luckily one car hire company had a German registered car which we could hire – at an extortionate rate. This change in the law has not been well publicised. Can you tell me what law this actually is?” she asked us.

She’s not alone. Few car hire firms appear to know anything about the change. On the Holiday Autos website this week, hirers making Swiss bookings were being warned only that they could not take the car into Albania and other non-EU countries. AutoEurope similarly made no mention of this significant new restriction in its terms when we looked. When we posed as a customer trying to make a booking, staff at the Sixt office at Zurich airport told us to note on our online booking that we intended to leave the EU, in which case we would be given a German-registered car. They couldn’t say why.

The European parliament office in London pointed us to a document entitled Commission Delegated Regulation (EU) 2015/2446, which details changes to yarn and to sugar. Let’s just say it’s not exactly comprehensible to the average reader. A European commission spokeswoman said: “EU citizens should try to inform the car rental company in advance if they intend to … drive into the EU. It is the responsibility of the company to provide a car that complies both with customs rules and also with traffic rules … Car rental companies in Switzerland are already providing EU-plated cars for EU citizens in order to comply with the new customs rules.”