The eldest daughter of IRA murder victim Jean McConville vowed to "name names" to police, as officers continue to hold Gerry Adams for questioning in connection with her kidnapping into a second day.

Helen McKendry's outspoken intervention came as the former Northern Ireland secretary Shaun Woodward warned that the arrest of Adams marks one of the most "tense and potentially quite dangerous" moments in the peace process.

Speaking to the Guardian McKendry, who has spent 20 years campaigning to bring her mother's killers to justice, said: "I spent the first 20 years of my life being afraid of these people, of fearing to speak out, but now I am no longer afraid."

McKendry, whose mother was dragged away by the IRA in 1972, said she was prepared to identify the abductors despite a fear or reprisals – in contrast with her brother Michael, who earlier in the day told the BBC he was not prepared to say who was involved.

She said: "If full cooperation into the murder of my mother includes naming those who burst into our flat, who dragged my mother away from us at gunpoint, and who were directly involved in her disappearance and murder, then yes – I would be prepared to name names. To me that is not informing but doing my duty to my mother."

McKendry said detectives had told the family that the Police Service of Northern Ireland has obtained as many as 11 tapes – testimonies from former IRA members – from a US academic archive relating to the McConville killing.

The continued detention of the Sinn Féin leader over the kidnapping, killing and secret burial of Jean McConville, a mother of 10, has thrown the delicate political settlement in the province back into crisis.

Woodward became the first senior political figure in London to raise concerns about the impact of the arrest. Labour's last Northern Ireland secretary told the Guardian: "This is a very serious and tense moment in the history of the peace process and the political process. So long as Northern Ireland continues to avoid having a mechanism to deal fairly with the legacy issues of the pre-1998 Good Friday agreement there will inevitably be these tense and potentially quite dangerous and threatening moments in the peace process and the political process."

His remarks came after Martin McGuinness said there were elements in the police force – which he and Adams once urged republicans to back – who were determined to hinder Sinn Fein's advance across the island of Ireland.

Northern Ireland's deputy first minister said his party had been told by "senior" and "reforming" elements within the PSNI that "there was still a dark side within policing here in the north of Ireland". He said: "I think we have seen that dark side flex its muscles in the course of the last couple of days."

Sinn Féin had earlier said that the arrest, weeks before the European parliamentary elections, was politically motivated – a suggestion David Cameron rejected. The prime minister said: "There has been absolutely no political interference in this issue. We have an independent judicial system, both here in England and in Northern Ireland. We have independent policing authorities, independent prosecuting authorities. Those are vital parts of the free country and the free society we enjoy today."

Matt Baggott, the chief constable of the Police Service of Northern Ireland, said the investigation would be "effective, objective and methodical".

Asked about the investigation, Baggott said: "Effective investigation applies to any unsolved matter and it would be inappropriate for me to comment on any individual investigation other than to say they will be objective and methodical."

Labour figures associated with the peace process made no criticism of the police who had, they said, followed the law. But Peter Hain, Tony Blair's last Northern Ireland secretary, said Adams had told him with great passion that he was not responsible for McConville's death.

Hain said: "Obviously the judicial process has to take its course. Gerry Adams has strongly asserted – as he always did to me when I was secretary of state and he was actually helping track the 'disappeared' – that he had nothing to do with this. In fact we actually discussed the Jean McConville atrocity because that is what it was – a terrible crime. He was passionate about it being wrong and he wanted to find out who was responsible – at least that it is what he told me and those of us seeking to address the 'disappeared' on behalf of the victims because there are many of them."

But Peter Robinson, Northern Ireland's first minister and key partner with McGuinness in the power-sharing executive, said the arrest strengthened Northern Ireland's political process. "I cannot say whether Mr Adams will be charged or released, whether he will be held for a further period, whether even if charged he might be convicted," he said. "But what I can say is that it strengthens our political process in Northern Ireland for people to know that no one is above the law – everyone is equal under the law and everyone is equally subject to the law."

The abduction, fatal shooting and covert burial of McConville, a 37-year-old Protestant who became a Catholic convert, continues to haunt both Adams and the peace process.

In front of her children at their home in the Divis flats complex, the West Belfast woman was dragged away by an IRA gang, driven across the border to the Republic, shot in the head at a remote coastal spot in County Louth, and then buried in secret.

She became the most famous of the "disappeared" – 16 IRA victims shot and buried at secret locations across Ireland during the Troubles.

Former IRA members including Adams's former friend, the hunger striker Brendan Hughes, have alleged that the future Sinn Féin president gave the order for McConville to be "disappeared" after she was shot as an informer. Her family have always rejected any suggestion that she was a British army agent pointing to Northern Ireland's former police ombudsman Nuala O'Loan's investigation, which found no evidence of their mother working as an informer.

Adams has consistently denied claims of involvement in the McConville murder or of being in the IRA. He was arrested on Wednesday evening after handing himself into the PSNI's serious crimes suite at Antrim Town. Before entering the police station, he repeated that he was "innocent of any part" in the murder.

The Sinn Féin leader spent Wednesday night in custody and could in theory be held until late on Friday under anti-terrorist legislation.

The allegations of a supposed police conspiracy against Sinn Féin and its party leader by McGuinness drew an angry response from the McConville family. The murdered woman's son-in-law, Seamus McKendry, who co-founded the campaign for the disappeared, described McGuinness's claims as "totally absurd and a deep insult to the family and the wider community's intelligence".

McKendry said: "This is the same PSNI which Martin McGuinness asked everyone including his own supporters to endorse when devolution was restored. He can't have it both ways. This is just typical spin to deflect from the real story behind all of this, to deflect from the terrible crime inflicted on Jean."

Ireland's prime minister, the Taoiseach Enda Kenny, dismissed any notion that the arrest was politically motivated.

"I hope the president of Sinn Féin, Deputy Adams, answers in the best way that he can, the fullest extent that he can, the questions being asked about a live murder investigation by the PSNI," Kenny said.His ministerial colleague Ruairí Quinn said any suggestion Adams was detained in order to interfere with politics south of the border was "ludicrous".

The arrest also refocuses attention on Sinn Féin's past connection to the IRA at a time when the party has been riding high in the opinion polls and seeking to make major gains in the Irish Republic's European and local government elections. Deputy party leader Mary Lou McDonald insisted that there was a political motive behind the arrest given that the country was only two weeks away from going to the polls.

• This article was amended on 13 May 2014. An earlier version said Helen McKendry had seen her mother being dragged away by the IRA. Although her brothers and sisters were present, she was not.