In a sunny park in Copenhagen, Mathias Buch Jensen was unimpressed. All around him, people were tucking into beer and chips. There were few signs that the latest offensive in the worldwide war on obesity was having much effect.

But then Denmark might not be the best place to experiment with a "fat tax" on lardy products. "You know, Danes are big fans of butter," Buch Jensen mused. "We love fat."

He added: "Knowing the Danes, it could have the opposite effect. Like naughty children, when they are told not to do something, they do it even more."

In a country known for butter and bacon, Denmark's new tax is a body blow. Danes who go shopping today will pay an extra 25p on a pack of butter and 8p on a packet of crisps, as the new tax on foods which contain more than 2.3% saturated fat comes into effect. Everything from milk to oils, meats and pre-cooked foods such as pizzas will be targeted. The additional revenue raised will fund obesity-fighting measures.

The move has parallels elsewhere in Europe. Hungary has recently imposed a tax on all foods with unhealthy levels of sugar, salt and carbohydrates, as well as goods with high levels of caffeine. Denmark, Switzerland and Austria have already banned trans fats, while Finland and Romania are considering fat taxes.

But it is Britain which has the biggest obesity problem in Europe, and campaigners have urged the government to follow Denmark's lead. Tam Fry, spokesman for the National Obesity Forum, said: "It is not a question of whether we should follow the Danes' lead – we have to. If we don't do anything about it, by 2050, 70% of the British population will be obese or overweight and that would result not only in the downfall of the NHS but also of our national workforce." A recent study found that poor health and obesity costs the UK economy at least £21.5bn a year.

Some experts argue that fat is the wrong target and that salt, sugar and refined carbohydrates should be tackled instead, but Dr Colin Waine, former chairman of the National Obesity Forum, welcomed the move. "All these things need to be looked at, but saturated fats have a higher calorie content than carbohydrates. I don't think you can do everything all at once."

Fewer than 10% of Danes are obese, below the 15% European average, according to the OECD. Britain's rate is 24.5%.

Buch Jensen, for one, is not planning to change his eating habits. Asked if he would be giving up butter, he offered a compromise: "I would fry cabbage in butter, and add a little more butter at the end. That way at least I'm getting my vegetables."