Senior officers are waiting for Supreme Court justices to decide whether the Police Service of Northern Ireland is sufficiently independent to carry out investigations into two events during the Troubles in Ulster half a century ago.

Seven judges based in London on Wednesday finished hearing arguments relating to proposed police investigations into the killing of a Catholic woman in 1972 and the treatment of 12 people, who have become known as the “hooded men”, detained in 1971.

Lord Hodge, Lord Lloyd-Jones, Lord Kitchin, Lord Sales, Lord Hamblen, Lord Leggatt, and Lord Burrows were asked to consider issues relating to the shooting of 24-year-old Jean Smyth in Belfast and the detention of the “hooded men”, following rulings by judges in Northern Ireland.

The seven judges, who oversaw a remote hearing which lasted three days, said they would deliver a ruling on a date to be fixed.

A barrister representing Mrs Smyth’s sister, Margaret McQuillan, and Francis McGuigan, one of the “hooded men”, told judges that the cases were of the “utmost seriousness”.

Hugh Southey QC said, in a written case outline, that one case concerned the fatal shooting of an “unarmed young mother”, in circumstances “implicating British Army personnel”.

He said the other concerned “state-sanctioned torture and/or inhuman and degrading treatment”.

Mr Southey said two issues arose in both cases, the “applicability of investigatory obligation” imposed by articles of the European Convention on Human Rights and the independence of the Police Service of Northern Ireland.

He argued that Mrs Smyth’s sister and Mr McGuigan were entitled to “effective, independent investigation” and told judges that the Police Service of Northern Ireland lacked the “requisite independence to investigate”.

Barrister Tony McGleenan QC, who represented the Police Service of Northern Ireland, told judges that the force did not lack the independence to investigate.

Amnesty International, which has supported a campaign by the “hooded men”, wants independent investigations.

Grainne Teggart, Amnesty International’s Northern Ireland campaign manager, said, before the hearing, that the “hooded men” case would be “hugely significant” to “torture victims across the world” and to the ongoing “unresolved issue of legacy of the troubles”.

Lawyers representing the Police Service of Northern Ireland had asked the Supreme Court to consider the case, following court hearings in Northern Ireland.

Judges heard arguments from lawyers representing Northern Ireland Secretary Brandon Lewis.