Berlin has become the first city in Germany in which rent-control legislation has come into force in a bid to put the brakes on some of the fastest rising rents in Europe.

From Monday, landlords in the capital will be barred from increasing rents by more than 10% above the local average. Such controls were already in place for existing tenants but have now been extended to new contracts.

“The rent ceiling is very important for Berlin because the difference between the rent paid in existing contracts and new contracts is so high,” said Reiner Wild, managing director of the Berlin Tenants’ Association. “The other problem is that we have 40,000 more inhabitants per year. Because of this situation the housing market is very strong.”

Berlin is pioneering the rent cap after the national parliament approved the law, aimed at areas with housing shortages, in March. Berliners say flat-hunting is becoming increasingly competitive.

“We were looking for the best part of a year,” said Vlasis Tritakis, a student. He, his partner Sofia and their 18-month-old son moved out of a flat-share into a one-bedroomed apartment in the district of Kreuzberg in April.

But sooner or later they will have to find a place big enough for his son to have a room of his own. They say they don’t stand much of a chance against competition from potential tenants with better finances. “I don’t know how we will do it,” said Tritakis.

Although rents are still low compared with other European capitals, Wild says it is vital to keep the city affordable for lower-income residents. “We don’t want a situation like in London or Paris,” said Wild. “The reality in Paris or London is that people with low income have to live in the further-out districts of the city.”

Wild said his organisation would like to see more action taken to address the problem, including the building of more affordable housing.

Kerstine Appunn and her boyfriend took three and a half months to land a spacious two-bedroomed flat in Prenzlauer Berg, one of Berlin’s pricier inner-city districts, where organic cafes populate the pretty, tree-lined streets.

“I heard that it was quite good going to find somewhere you really like without making too many compromises in such a short time, and in such a nice area,” Appunn, a journalist, said. “But I guess we are paying for it. It is quite expensive for Berlin.”

Average rents in the German capital rose from just over €5.50 (£3.60) a square metre in 2005 to close to €9 last year, according to a report by property services company Jones Lang LaSalle. Between 2013 and 2014, rents went up by more than 9%.

Lance Anderson, a translator, arrived from the UK in 1998. He moved into a two-bed flat close to Potsdamer Platz, in the heart of the city, six years ago, before “things went crazy” in terms of rent rises.

“I used to be able to pay my rent for the whole month just by working one shift as a waiter,” he said of his housing situation in 2003, when he lived in a shared flat in a now very desirable neighbourhood on the eastern edge of Kreuzberg.

He conceded that the flat was heated with coal stoves and said it was directly above a flat that a neighbouring tenant rented just for his dogs. But Anderson also says Berlin’s much-bemoaned gentrification has had its benefits: better places to eat out; more diverse, international communities; and the pleasant feeling of living in a lively, populated city.

But he says it is difficult to adjust to the rapid rise in rents in a city where wages are still low. “All my friends who have been in the city a long time have old leases – we know we cannot afford to move,” Anderson said.

“We are stuck in our flats, kind of like polar bears on our little ice sheets. It sounds like a privileged position to complain about, but for example for couples wanting to move in together – it’s like: ‘Well, can we really afford to?’”

• This article was amended on Wednesday 3 June 2015 to correct a misspelling of “brakes” in the opening paragraph.