Kopenhagener Strasse is a quiet street in the Prenzlauer Berg district, just a few metres east of where the wall used to run. Most of the tenement houses that flank the cobbled street here were built during Berlin's big push for industrialisation in the late 19th century, as a counter-statement to the social segregation that Friedrich Engels had reported from Manchester: let's bring white and blue collar workers under one roof – that was the intention, at least.

These days, the houses on Kopenhagener Strasse are still not too far from meeting that ideal. At No 46, the front house is occupied by students and media professionals. In the set-back building that curves around the communal yard, a nurse and her family live on the same floor as pensioners and artists. Rent is still relatively low: one couple, who have lived here since 1962, are rumoured to pay €100 (£83) a month.

But recently things have changed at No 46. A year ago, the apartment block was bought by Wulf Christmann, an investor who already owns a number of properties around Berlin. Four months later, a letter arrived: urgent renovations including a new central gas heater, triple glazing and upgraded insulation were announced – the kind of green measures the German government is keen to promote, and which local councils thus tend to wave through without hesitation. The catch was hidden at the back of the document: charges amounting to a permanent rent increase of more than 300%.

Ottmar Mayer, a 73-year-old pensioner who lived in the rear building, used to pay around €370 a month for his three-bedroom flat – now he was suddenly looking at over €1,200. "Well people, shouldn't we just accept this very humane offer and finally live in a luxury home like normal people?", he wrote on the apartment block's own blog in September. His sarcasm may have masked a genuine anxiety. A month after writing his blogpost, Mayer died from the result of a long-running heart problem. Neighbours say he had been having trouble sleeping.

In the rest of Europe, Berlin still enjoys a reputation as a renters' paradise. Without an appropriately sized airport and a financial industry to drive up house prices, the German capital has for centuries been a cheap place for Europe's bohemian and artistic avant garde to live.

Mortgages have traditionally been hard to come by in Germany and tenants are still relatively well protected by the law. Accordingly, home ownership rates, already low across Germany, are even lower in the capital: in 2011, 15.6% of Berliners owned their own place, compared with 49.5% in London.

The back courtyard at 46 Kopenhagener Strasse, Berlin. Under the guise of 'renovations' to make buildings more environmentally friendly, landlords are pushing up rents. Photograph: Guardian Cities

But many Berliners fear that the city's status as young Europeans' destination of choice is destroying what made it so attractive in the first place. Rents in Berlin have risen by 28% since 2007, and are continuing to climb at almost twice the national average. In its monthly report in October, the Bundesbank said that properties in large German cities like Berlin "may currently be overvalued by between 5% and 10%".

One property, an apartment block on Linienstrasse in Berlin Mitte, gives an alarming vision of Berlin's future: its value has multiplied tenfold since 1997. Then sold for the equivalent of €700 ,000, it has passed hands four times since and was last on the market for more than 8m euros.

Stories like Mayer's are neither new or rare. Many elderly men or women who are forced to move out of their three-bedroom flats because of "renovation" measures realise that they can't afford a one-bedroom flat in the same area.

Berlin's social housing stock is falling just as the demand is rising. According to Hanover's Pestel Institute, the German capital needs an additional 500,000 affordable homes, but the city hasn't built new social housing since the early 2000s, and at the current rate it would continue losing around 4,500 homes a year.

Currently, the city senate claims to have found funds to support the building of around 1,000 affordable homes this year. But whether they will be in the centre or towards the Brandenburg outskirts, remains unclear.

"The danger for Berlin is not that it will become like London, but that it will become like Paris, with the poor and elderly carted out to the edges of the city", says Andrej Holm, a sociologist who writes a blog on Berlin gentrification.

Unlike some critics of Berlin's growing appeal to tourists, he is happy to admit that Berlin has also benefited from gentrification. Twenty years ago, parts of now trendy Prenzlauer Berg used to have streets without streetlights, apartment blocks that only had outdoor toilets, and flats heated with coal ovens. Now many parts of the area look more modern than those in the old west of the city.

The real threat facing Berlin at the moment, he says, is not gentrification, but "gentrification without a rise in living standards". Incremental reforms of German tenancy law have enabled landlords to force through "energetic modernisations" of their properties and pass down up to 11% of their costs to the tenants. In upcoming areas such as Prenzlauer Berg, Neukölln and Kreuzberg, there have been numerous reports of landlords abusing the "energetic modernisation" rule: flushing out old tenants by announcing expensive renovations, only to then immediately put the flats on the market at a higher price without having made any significant improvements.

The apartment block at No 46 Kopenhagener Strasse, Berlin. Photograph: Guardian Cities

Since a number of these cases have gained attention in the media, the German government has promised a crackdown on such practices. The coalition agreement between Angela Merkel's Christian Democratic Union party and the Social Democrats includes a pledge to bar landlords from signing new leases with rents that are 10% above the neighbourhood average, according to the guide to rental rates, the Mietspiegel (literally meaning "rent mirror"). Another cap would limit the period over which renovation costs can be passed down to tenants to 10 years – currently they can be passed down indefinitely.

Whether such proposals will solidify into legislation remains to be seen. Both investors and gentrification critics like Holm remain sceptical. They predict a gradual decline of the German tendency to favour renting and a growth in home ownership, especially in trendy areas such as Prenzlauer Berg. The poor and the elderly will be unaffected by the new rent cap – what they need is housing which is not at, but well below, the neighbourhood average.

At 46 Kopenhagener Strasse, such measures are likely to come too late at any rate. A few tenants have rejected the owner's renovation measure and may end up facing their landlord in court. But others won't have the stomach, or the financial means, for a big fight. Last weekend at No 46, the first family decided to move out.