Philomena is a small film that is defying box-office conventions; the audience keeps on growing while other, bigger titles fade. The emotional story starring Steve Coogan and Dame Judi Dench of the brutal separation of an Irish mother and her child has become a word-of-mouth hit, beating even action blockbuster Thor: The Dark World at the UK box office one day last week.

Now Philomena's trenchant message is having an impact on the personal lives of many families in Ireland; families who believe that they were also the victims of church dogma – their babies taken away because their unmarried mothers were judged immoral.

The performance by Dench, who has become internationally famous playing James Bond's steely boss M, is expected to win nominations for a string of acting prizes in the coming awards season. It has also reignited the controversy in Ireland about the damage done when so-called "stolen babies" were offered by nuns and Catholic institutions to couples living as far away as the US.

Adoption rights organisations in the republic say calls to their offices in Dublin and hits on their Facebook pages have trebled since the film opened to critical acclaim at the beginning of the month.

The real-life story of Dench's character, Philomena Lee, has prised open a scandal that campaigners say will be even bigger than the enslavement of teenage girls in the Catholic church-run Magdalene laundries, or the abuse of boys in Ireland's notorious industrial schools.

Meanwhile the children of thousands of other "Philomenas" appealed this weekend to Dench to call for an Irish state inquiry into the scandal. They want the veteran actor to champion their cause across the world and at award ceremonies such as the Oscars.

And on Saturday Coogan, her co-star and one of the film's writers, said: "I will absolutely do anything to help them. The church reaction has been same old, same old. I am happy to wade in."

The Adoption Rights Alliance has reported a threefold increase since the film was released in calls from children who were adopted.

Under the direction of Stephen Frears, Dench is shown searching for the son she was forced to give up for adoption while living in a convent for "fallen women" 50 years earlier. Coogan, who co-wrote the screenplay with Jeff Pope, plays the journalist Martin Sixsmith, whose 2009 book The Lost Child of Philomena Lee described his own efforts to help Lee track down her long-lost son.

Susan Lohan, who co-founded the Adoption Rights Alliance and was taken away from her mother in 1965, said so-called "banished and stolen babies" would be delighted if Dench spoke out for their campaign for justice.

"We would like her to announce to the worldwide TV audience that the practice of unlawful containment of unmarried women and girls in these mother and baby homes has never been investigated by the Irish state.

"There was no apology nor has redress ever occurred. Incredibly, the Irish state continues to fund its partner in crime, the Catholic church, to hold the birth and care records of over 50,000 children. The state colludes with them to prevent the 'taken children' from discovering their identities," she said.

Lohan, who lives in Malahide, north Dublin, eventually found out that her mother was a 30-year-old civil servant who had been forced to give her up. The adoption rights activist encountered further problems tracing her father. As late as 2001, Lohan said a nun whose order organised the adoption accused her of being a "destroyer of lives" by seeking to track down her father.

"We desperately want Dame Judi to highlight that, if Anthony Lee were looking for his mother Philomena today, he would face the same problems as shown in the film.

"Because the bad guys in this story, ie the religious orders of nuns, have only recently dumped their records with an under-resourced HSE [Health Service Executive], which has no resources to safeguard the records, never mind quantify or identify the data held within."

In terms of size and social impact, Lohan predicts that this "third scandal" involving the state, Catholic institutions and the maltreatment of children will eventually eclipse all the others.

"The issue in Ireland is nuclear," she said. "It will dwarf the numbers involved in the Magdalene laundries. It also implicates so-called pillars of Irish society such as politicians, public servants, solicitors, nurse, doctors, midwives and social workers. The so-called nice middle-class people who knew about, who arranged, who funded and who were directly involved in forced adoptions."

However, Mannix Flynn, a Dublin city councillor and former child inmate of the industrial schools, said the movie had failed to examine the role of the Irish state in "abducting these babies from their mothers and as a result has let it off the hook".

Flynn added: "The film is politically naive and I fear that people on seeing it around the world will conclude that this is a scandal that was part of Ireland's past. But the scandal is present day because there has been no accountability, no inquiry and no one paying their dues to what was done to these mothers and their babies."

But Lohan said the film had bolstered those who were forcibly adopted to fight on for truth and justice.

"It has crystallised our own grief at the loss of our mothers and our anger at the state's and the church's ongoing campaign to prevent us from reuniting with our mothers," she added.

And last week, despite its challenging subject matter, after two weekends in the UK's cinemas Philomena had grossed £4.76m. This means that it has moved ahead of Frears's other recent hit film, The Queen, starring Helen Mirren as Elizabeth II, which had made £2.66m at the same stage of its run.