Membership of the European Economic Area (EEA) may not be the “right solution” for the UK after Brexit, the prime minister of one of its key members has said.

Icelandic prime minister Katrín Jakobsdottir expressed hesitancy at the idea that Britain could join the EEA, suggesting that the debate in the UK was far from the realities of the agreement.

She was in Brussels to meet her EU counterparts for a celebration of 25 years of the EEA’s existence – joking that “maybe some of the EU leaders have other things on their mind” after a late night Brexit negotiation that spilled over into the early hours of the morning.

“What do I advise Mrs May?” Ms Jakobsdottir, who is from Iceland’s left-green party, said when asked by reporters on arrival at the meeting.

“I don’t know if our circumstances are fitting for the UK. Obviously the discussion there isn’t maybe exactly what the EEA agreement is about.

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“We’re members of the four freedoms, people, movement, services and all that. I don’t know if that’s the right solution for the UK.”

She added: “But I think it’s very important for the UK as well as Iceland to think about how we can progress with our European cooperation which has been very important for Iceland.”

The European Economic Area replicates most aspects of the EU’s single market – including freedom of movement of people and goods. Some campaigners have suggested that the proposal, sometimes terms “the Norway option”, would be a good compromise in a country split down the middle on the question of Brexit.

Norway’s prime minister Erna Solberg, who was also at the summit, said the EEA had been “of benefit to us all” and that the “agreement ad contributed to securing welfare and jobs both in the EU and in Norway”.

The glowing picture painted of the arrangement by Ms Solberg, a conservative, was a far cry from the one she painted before the UK’s 2016 EU referendum, when she described the EEA’s arrangements as “frustrating”.

Some EU leaders appeared to nudge Britain towards the Norway model, however. After the celebration, Irish prime minister Leo Varadkar tweeted: “Good to meet up with the Norwegian, Icelandic and Liechtenstein prime ministers. All in the single market for 25 years but not in the EU. Sensible solutions are possible once red lines don’t restrict them.”

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Theresa May left the summit early in the morning after securing an extension to Article 50 on Thursday night, and did not attend the EEA celebration.

The EEA would require the UK to be aligned with EU rules but have little say over their formulation. It does not include a customs union, and as such would not alone provide frictionless trade – though Brussels has suggested such a double arrangement could be considered if the UK decided it wanted one.