And the European film market is expected to continue growing for another four years, when it will be worth 7.4bn euros (£4.75bn), according to trade publication Screen International's website.
Harry Potter and the Philosopher's Stone and The Lord of the Rings were the most successful films around the world in 2001.
But home-grown films also performed well, and the growth of multiplex cinemas did not mean that European screens were swamped with mediocre Hollywood releases, according to the report by box office analysts Dodona Research.
"Contrary to popular belief, multiplexes have not caused further Americanisation of European cinema," the report said.
More than three-quarters of European cinema admissions were in just five countries - the UK, France, Germany, Italy and Spain.
But smaller countries saw the biggest growth.
Portugal's box office takings showed the largest increase, surging by 255% between 1995 and 2001, according to Dodona Research.
The Czech Republic was next, with 229% growth, while Poland's box office takings rose by 214%.
Rising living standards
The UK showed the biggest growth of the "big five" countries, which also include France, Germany, Italy and Spain, with British ticket receipts up 147%.
The average across 21 European countries was 76%.
Hungary, Poland, the Czech Republic, Romania and Greece are expected to show the biggest box office growth over the next few years.
Multiplexes were not as important to the growth as many in the industry thought, the report said.
Instead, it was down to rising living standards and increased leisure spending, it added.