There's not really much you can do except suck it up.
On my recent trip to Denmark, I paid by cash everywhere as I could not be sure I wouldn't be charged this fee. Perhaps surprisingly, I had no problems spending cash and there was no reluctance by any merchant to accept cash.
The only mild hiccup was near to Copenhagen H just before my train to Hamburg. I went to a bakery to get some food for the journey. On asking if they were happy to take cash, they said yes but they had no change. Fortunately this was ideal for me as I wanted to get rid of all my coins anyway, so just had to select items that added up to the amount of coins I had. When they opened the till I saw it was completely empty with no cash at all.
Does the tax increase on expensive purchases ? Is it applied to a hotel pre paid from the UK on card ?
It's not a tax it's a bank fee that the merchant terminal adds on when it detects a certain type of card. Hotels are unlikely to pass on fees as they are aware they have guests from all over the world.
That's interesting. So the bill is 140, the cashier says 140, the card terminal (which doesn't yet know you're about to present a foreign card) says 140.
At what point do you get notified that it's going to be more? Does the terminal show the new price, or is it only when the receipt's printed, and it's too late?
This situation is very common in Australia at almost every restaurant / bar / cafe as well as random smaller shops, and it applies to all cards, not just foreign ones.
The card terminal says $50. After you tap a card or device the amount changes to some random number such as $51.63 and that's what you get charged. Sometimes, inserting a local debit card and using the PIN will not attract an additional charge, but it depends on what the merchant has set up.
This is curently legal even when there is no way to pay without a card surcharge. In theory merchants can only pass on what they actually get charged by the bank, and must inform you of the amount of surcharge as well as display the total price including surcharge if it's unavoidable.
But walking through any shopping centre in Australia will find numerous breaches of the rules, while the enforcement body does not take action on individual complaints, and consumers need to be very dedicated to bother initiating chargebacks over a few cents.
The central bank intends to ban fees on Visa and Mastercard from October, but roughly 1/3rd of Australians are opposed.
A similar situation occurs in New Zealand. Oddly NZ only proposed to ban surcharges on in-person payments while permitting them for online payments, but there was enough opposition that legislation has been halted for more consultation.