Sitting on a wooden bench on a Dresden square with his jacket collar turned up against a cold evening wind, a retiree in his mid-sixties with a dog by his side starts a conversation with a couple in their early thirties. “I used the dog as an excuse to take a look at what’s going on here,” he says, squinting and drawing on a cigarette. “I’m not a political animal at all. The wife doesn’t know I’m here.” The man and woman, dressed in cashmere scarves and coats by a popular outdoor clothing brand, seek to reassure the newcomer. “This is our third time. We were nervous at first until we realised how many other people like us were here, demanding a proper asylum policy, one that doesn’t disadvantage native Germans,” the woman says.

The pensioner’s mind seems to have been put at ease. When the protest started moving through the city, eerily silent – at the explicit request of organisers – he and his Jack Russell join in.

The encounter (none of those involved wished to give their names) occurred at the sidelines of a recent rally organised by Pegida, or Patriotische Europäer gegen die Islamisierung des Abendlandes (Patriotic Europeans against the Islamisation of the west), a populist anti-immigrant movement that has been galvanising support in Germany for several months but has convulsed the city of Dresden in particular. Having begun on Facebook, on Monday it will hold its 11th demonstration in the baroque city and it is estimated that more than 20,000 will attend.

As the movement spreads across Germany and even into other parts of Europe – Sweden, Austria and Switzerland – politicians of the country’s mainstream parties are on alert.

As the group grows in stature, so too does opposition to it. On Monday the lights of Cologne cathedral will be turned off in a mark of the church’s disapproval of a Pegida rally there, which is expected to bring thousands on to the streets.

Pegida participants feel buoyed by the fact they are part of a growing movement across Europe of voters who feel that mainstream politicians are far too lenient on immigration. At a typical Pegida rally, supporters talk of their anger that Germany is being overrun by Muslim immigrants; they say many are criminals who need to be deported immediately and they call for an obligatory integration programme. Banner slogans read: “We want our homeland back” and “Send the criminal asylum seekers packing”.

Fears among chancellor Angela Merkel’s conservative alliance were already rife that it is losing considerable support to the budding Eurosceptic, and ever more anti-immigration, Alternative für Deutschland party (AfD). Merkel herself has been accused of creating a vacuum on the right due to her consensus style of politics, which the AfD, and now Pegida – to whom the AfD has openly given its backing – have willingly managed to fill.

The growth of Pegida has only increased calls for the government to tighten asylum rules and speed up the deportation process to appease voters. With so much pressure from within her own ranks, Merkel’s hard-hitting reaction to the group last week was therefore bold and surprising. “I say to all those who go to such demonstrations: do not follow those who have called the rallies, because all too often they have prejudice, a chilliness, even hatred in their hearts,” she said in her televised address to the German people.

Merkel, who has previously warned Pegida followers against allowing themselves to be manipulated by the organisers, with remarks that seemed like thinly veiled references to the Pied Piper of Hamelin, was also full of condemnation for their misuse of the slogan “Wir sind das Volk” (We are the people). The punchy phrase was adopted by East German anti-communist demonstrators in the runup to the fall of the Berlin Wall, and now punctuates Pegida rallies at regular intervals.

But, said Merkel, who spent the first 35 years of her life under communism, far from being an expression of the wish to unite, as it was in 1989, the phrase was now being used to divide. “What they really mean is ‘you are not one of us’, because of your skin colour or your religion,” she said.

The precipitous rise of Pegida has shaken Germany’s main parties to the core and prompted an acrimonious debate at a time when Europe’s biggest economy is straining to deal with a record intake of more than 200,000 asylum seekers in 2014 – mainly from Iraq and Syria – a figure higher than any other country in Europe and which is due to rise considerably this year.

Chancellor Angela Merkel has been forced to go on the attack against Pegida. Photograph: Maurizio Gambarini/AFP/Getty Images

Merkel’s condemnation of the group gives voice to growing concern among established parties in Europe about the impact immigration is having on domestic politics, in what will be a crucial election year across the continent.

This week Merkel will travel to London for talks with David Cameron. While the main thrust of their discussions will be on Russia and Ukraine and the economy, the two will probably not be able to avoid talking about the rise of parties such as Ukip and AfD/Pegida, or Cameron’s plans to curb migration from Europe as he seeks to renegotiate the terms of the UK’s EU membership.

Merkel will visit the British Museum’s exhibition, Germany: Memories of a Nation, a trawl through 600 years of German history, which inevitably gives space to the war – one of the most striking exhibits is the gate of Buchenwald concentration camp – and will further remind Merkel why immigration is so important for her country’s image of itself as a modern, progressive and welcoming land. But it is an image that is under threat.

Monday’s Pegida demonstration will be extremely closely observed, by everyone from constitutional experts to sociologists and experts in neo-Nazism. The questions most frequently addressed are what has prompted Pegida and how it can be dealt with. To condemn it means potentially isolating voters and fuelling the movement even more. But to ignore what is after all still a fledgling movement with no mandate seems too perilous a position for German politicians duty-bound to keep in mind the country’s Nazi past.

Already there are suggestions, so far unfounded, of a link between the recent apparent arson attack on a hostel for asylum seekers near Nuremberg, which was daubed with swastikas and anti-immigration slogans, and a pre-Christmas graffiti onslaught on a mosque in Dormagen in North Rhine-Westphalia, which was also smeared with swastikas and slogans such as “Get yourself to concentration camp” and “Waffen SS”. Such incidents have only served to stoke the tension.

Of particular concern are the numbers of participants at Pegida rallies who have far-right connections. Its followers include known neo-Nazis, including members of the National Democratic party (NPD), which until recently had seats in the regional parliament, and at least two football hooligan organisations called Faust des Ostens (Fist of the East) and Hooligans Elbflorenz (Florence of the Elbe Hooligans). At the demonstrations they mix with middle- and working-class Germans. The rules everyone is apparently asked to abide by are: don’t drink, don’t be violent, don’t talk to the press, and walk in silence, on what are euphemistically referred to as the group’s “evening strolls”. Before Christmas it held a carol service in front of Dresden’s opera house.

“We are here to assert our rights,” says one middle-aged woman. “Germany feels like a foreign country. We’ll be obliged to read the Qur’an before long,” she jokes to her companion. But immigrants in the state of Saxony, of which Dresden is the capital, make up just 2.8% of a population of 4 million (compared to around 14% in Berlin). Just 0.1% of those are Muslims. Why does she feel so alienated? “Well, we look at cities like Berlin and Hamburg, and we think: we must avoid such scenarios here,” she explains.

Her companion, a man in his fifties, also refused to give his name to the “Lugen Presse” (liar press, a term coined by the Nazis and frequently chanted at Pegida events), but is quick to add: “We’ve nothing against helping foreigners in need, like those poor people in Syria, but we should be helping them in their own country, not bringing them over here.”

The demonstrations feel like an invitation for anyone to voice any grievance. They are said to attract Germany’s growing number of so-called “Wutbürger” or angry citizens. Alongside people campaigning against factory-farmed chickens are those calling for the abolition of the television licence or protesting against Nato’s “aggressive stance” towards Russia.

Some plead for the return of their “Heimat” or homeland from the grip of foreigners. One man, carrying a large German flag which flaps in the wind, is heard greeting his friends with “Heil Deutschland” to be met by peals of laughter.

At the centre of it all is Lutz Bachmann, a 41-year-old former sausage vendor turned advertising agent, whose Facebook page boasts of his pet Jack Russell, Bärbli, and his honeymoon in the Dominican Republic. He prompts much applause and laughter from his audiences as he addresses them from a mobile caravan.

“Germany is not a land of immigration,” he tells the crowd. Dressed in a parka and sporting a stubbly beard, he calls on those who he says have been sacked from their jobs for belonging to Pegida to show courage, and dismisses those who have called the demonstrators “losers” or described them as being full of Abstiegangst (the fear of descending the social ladder). “No,” he says. “We just want Germany to stay German!”

The leader of Pegida, Lutz Bachmann, delivers a speech during a rally. Photograph: Jens Meyer/AP

Bachmann, the son of a Dresden butcher, has a criminal record for breaking and entering and drug possession, for which he was sentenced to 44 months in prison. He fled to South Africa, but was deported to Germany two years later. The affair is dismissed by his supporters, despite their frequent references to “criminal asylum seekers”. “It’s not like he killed anyone or abused a child,” one female rally participant says. “We all have pasts that we have to live with,” says another.

Across Germany, counter demonstrations have been held every Monday to coincide with Pegida’s gatherings. In Munich last week cultural figureheads drew a crowd of 12,000 under the banner “New York, Rio, Rosenheim – the World is Large Enough”, who together sang Beethoven’s Ode to Joy.

The anti-Pegida voice is keen to stress that Germany is in danger of losing a reputation it has established over the past decades which reached its apogee first when Germany hosted the World Cup in 2006, and again last summer when the national team won the championship.

“When we won the World Cup, it felt great to be able to fly the German flag with a certain pride again, without feeling embarrassed for the war and all that,” says Julia Schenck, 32, a psychologist taking part in a recent counter-demonstration in Dresden. “People outside Germany were celebrating our openness and warm-heartedness. But it feels now like we’re regressing. There are many people who would like Germany to return to the era around about the 1950s before we were a land of immigration.”

But others argue the situation is far more positive, and that Pegida has emerged as a side-effect of a growing sense of German empathy and solidarity towards outsiders, as immigration charities report a surge in contributions, and as increasing numbers of small German towns and villages, and many private households, take in refugees, many for the first time since the second world war.

“We’re seeing a growing emotional willingness among people in Germany to help others who are in need,” says Heinz Bude, a leading macro-sociologist at Kassel University. “The decisive question being asked by many right now is, do we just want to stubbornly focus on our own interests or, as the richest, perhaps also most powerful, society in Europe, are we willing to be generous towards others and to offer them help?”

Many are choosing the latter, he suggests, and Pegida is just the “response to the new-found spirit of hospitality”.