Liam Byrne, a key member of the Kinahan organised crime gang, has claimed his extradition to the UK should be rejected because he risks "inhumane and degrading treatment" in a British prison.
The claim is one of the key arguments put forward by his lawyer in a Spanish court, arguing the extradition order should be refused.
Byrne's counsel, Jaime Campane, told the court there is a "real risk" that his client's fundamental right to physical and moral integrity will be in danger if his extradition to the UK goes ahead.
He said the approval would violate his human rights because the only evidence against him is hacked messages on encrypted communications network Encrochat, Mr Campane claimed.
The appeal against the extradition order came before Spain’s Audencia Nacional court last week.
Byrne, who was arrested on June 4th in Alcudia following a UK-issued international arrest warrant, watched the proceedings via videolink from the prison near Palma.
A separate extradition appeal for suspected Kinahan gang member Jack Kavanagh was also held last week.
Spanish prosecutors formally backed the extradition of both men, who are wanted on suspicion of firearms offences.
Kavanagh, who was arrested at Malaga Airport on May 30th while transiting from Dubai to Turkey, remains at a prison on the Costa del Sol while he awaits a ruling in the matter.
On Monday, it emerged the decision is likely to be delayed due to a formal request which has been sent to Irish authorities asking them if they wish to prosecute the two men.
The request is linked to a 2016 ruling on extradition requests made to EU countries by so-called 'third countries' outside the EU which now applies to the UK following Brexit.
Mr Campaner cited overcrowding in some UK prisons among the reasons why Byrne’s well-being would be put at risk if his extradition is approved.
He has also flagged the recent escape of terror suspect Daniel Khalife from Wandsworth Prison, which raised questions about staff shortages and conditions at British prisons.
Mr Campaner told the court it should refuse the extradition request if Irish authorities decide not to extradite him.
He said if the decision goes against Byrne, the UK should state in which prisons he will be held.
The UK's National Crime Agency alleges the men were part of a plot spearheaded by Jack’s father, Thomas ‘Bomber’ Kavanagh, to plant arms in Northern Ireland and direct authorities to find them so he could get a reduced sentence on drug charges he was facing.
Thomas Kavanagh recently received a 21-year jail sentence for drugs and money-laundering offences.
Jack Kavanagh’s appeal against the UK extradition order was initially due to go ahead on September 11th before it was suspended following a no-show by his lawyer.
Spanish state prosecutors had laid out their case for his extradition in a six-page document presented to the Audiencia Nacional before the suspended hearing.
Prosecutors alleged Jack Kavanagh used the Encrochat encrypted communications network to participate in criminal activities.
Following the arrests, the region head of investigations at the NCA Kay Mellor said: "This investigation is part of the NCA’s ongoing work targeting the Kinahan crime group.
"Liam Byrne and Jack Kavanagh have been evading justice for a number of years, but have now been arrested in relation to serious firearms offences.
"We have an excellent relationship with the Spanish National Police and will continue to work closely with our international partners to ensure those who think they can stay under the radar have no place to hide."