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

Seven judges based in London are 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, at a remote hearing due to end on Wednesday.

Lord Hodge, Lord Lloyd-Jones, Lord Kitchin, Lord Sales, Lord Hamblen, Lord Leggatt and Lord Burrows, have been 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.

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”.

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 the legacy of the Troubles”.

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

Judges are also hearing arguments from lawyers representing Northern Ireland Secretary Brandon Lewis.

A Supreme Court spokeswoman said, in a written explanatory note, judges would consider whether the Legacy Investigations Branch of the Police Service of Northern Ireland was “sufficiently independent” to investigate Mrs Smyth’s death, or other “such deaths”.

The spokeswoman said an investigation was planned by the Police Service’s Legacy Investigations Branch but, before it began, Mrs Smyth’s sister had taken legal action and raised issues relating to independence.

She said judges would also consider whether the Police Service of Northern Ireland was “sufficiently independent” to carry out “any necessary investigation” into the treatment of the “hooded men”.