None of the IRA's "on-the-runs" who hold police letters promising immunity is safe from arrest, the Northern Ireland secretary is to say.

In a speech at lunchtime on Friday, Theresa Villiers will say that even the 187 IRA "on-the-runs" – members who are wanted in either Great Britain or Northern Ireland for crimes committed during the Troubles between 1969 and 1998 – would not be immune from future arrests or detentions.

Villiers will tell a gathering of European journalists in Belfast that "no-one holding one of these letters should be in any doubt, they are not 'get-out-of-jail-free cards'".

"They will not protect you from arrest or from prosecution and if the police can gather sufficient evidence, you will be subject to all the due processes of law, just like anybody else.

"The letters do not amount to any immunity, exemption or amnesty … something that could only ever be granted by legislation passed by parliament."

While in power, Labour attempted in 2005 to introduce legislation to grant immunity from prosecution for IRA fugitives who were wanted in the UK for past crimes. When the opposition scuppered the legislation after objections from Dublin and the nationalist SDLP, Labour created a secret scheme giving 187 IRA "on-the-runs" the letters of assurance.

The existence of the letters was revealed at the Old Bailey two weeks ago when defence lawyers produced one held by John Downey, a convicted IRA member who was standing trial for the 1982 Hyde Park bomb atrocity. As a result of the letter being produced in court, the case against Downey collapsed.

Villiers will say: "No letters have been issued by the Northern Ireland Office since December 2012 … and as far as this government is concerned, the scheme is over.

"If at any time we had been presented with a scheme that amounted to immunity, exemption or amnesty from prosecution … implied or otherwise … we would have stopped it immediately. My party and this government do not support – and have never supported – immunities, exemptions or amnesties from prosecution."

On the Downey case specifically, Villiers will say: "It was the fact that the letter he was sent was factually incorrect and misleading that led the judge to rule that an abuse of process had occurred. John Downey should never have been sent a letter saying he wasn't wanted by the police because at all times he was wanted by the Metropolitan police in relation to the Hyde Park bombing."

The Northern Ireland secretary has pledged to put an end to "the era of secret deals" in the peace process.

Villiers will also welcome Labour's apology this week for the way the scheme was concealed from other politicians in Northern Ireland and the Irish government of Bertie Ahern.