Concern is growing in Norway and Iceland about how to respond if the UK’s House of Commons votes to apply to join Efta, the four-nation European free-trade association of which both countries are members.

While the plan appeals to a growing cross-party lobby of British MPs, who see Efta membership as a compromise solution to leaving the EU yet keeping the UK’s close economic ties with the European single market, it has divided opinion within Efta member states.

Iceland’s foreign minister, Guðlaugur Þór Þórðarson, a free trader, enthusiastically backed British membership of Efta on a visit to London this week. But he said it would be a challenge if the UK also sought to stay in the EU customs union, as proposed by the chief backers of the Norway option in the Commons. For British MPs, membership of the customs union would ease concerns over the border in Ireland.

The four Efta members, Norway, Iceland, Lichtenstein and Switzerland, currently strike their own free-trade deals with third countries outside the European Union, but the UK, if it negotiated to stay inside the EU customs union, would be excluded from doing this. This would reduce the chance of Efta becoming a large and attractive trading bloc, one of the advantages of Britain joining Efta from Iceland’s viewpoint.

Speaking on BBC Radio 4, Þórðarson said he was not sure why the UK should wish to join the EU customs union after Brexit and added that any such decision would represent a challenge for Iceland.

Iceland’s prime minister, Katrín Jakobsdóttir, was more wary about the UK joining Efta last week, stressing that the UK would need to accept free movement of labour.

But in Norway, probably the single most influential country inside Efta, opinion appears to be hardening against UK membership as the option grows more likely. The concern is expressed openly by the opposition Labour party, and more warily in government circles.

Anniken Huitfeldt, head of the Foreign and Defence committee and a Labour member, said she was not interested in the UK joining either Efta or the European economic area, the single market grouping that assembles the EU and and Efta members. She said: “We do not encourage them. It is not in Norway’s interests to bring Britain into the EEA … The UK should never have voted to leave the EU in the first place.”

The leader of Norway’s opposition Labour party, Jonas Gahr Støre, speaking to the Guardian, expressed his doubts about UK membership of Efta or the European Economic Area. He said: “All decisions are taken by consensus and it is not obvious that Britain and Norway would see eye to eye on all decisions that came from Brussels regarding the internal market. There is in the political debate in Norway a concern that a British presence could make our relationship more unstable, and I think that is reflected in the statements made by the current government and the opposition

“Norway would like to see smooth, open and friendly relations with our partners across the North sea. Whether that objective is secured by the UK joining Efta or the EEA is a different question.”

He pointed out that after 40 years of membership of the European Union and after 2016 referendum, the British would by joining the EEA “be gaining a new set of obligations but with far less influence and codetermination”.

The head of Norway’s business group NHO, Tore Myhre, last week also urged the country not to reopen the agreement by inviting the British into Efta. He said: “Norway’s existing deal is fragile and it is important for us not to put it at risk.”

Norway’s foreign minister, Ine Eriksen Søreide, pressed on TV last week to say whether she would support a British application to join Efta, avoided the question, focusing on the need for an orderly Brexit.

Similarly, appeals by British MPs that support the Norway option for the Norwegian government to make a public invitation to join Efta have been spurned by ministers anxious not to be seen to be interfering inBrexit politics.

Some Norwegian officials say privately that the underlying fear of British Efta membership is that the UK would dominate the organisation, and therefore its negotiations with the EU. One concern is that Norway might have to renegotiate its existing trade deals if the UK became a member.

Moreover, it might cast a disruptive light on an arrangement that despite its democratic pitfalls has worked for Norway’s economy by providing access to the EU single market, excluding agriculture and fish.

Norway, a country that tries to operate by political consensus, has long accepted an uneasy compromise in which it accepts the four EU freedoms, including freedom of movement, but remains outside the EU, as its citizens voted twice in referenda to reject EU membership. One official said: “There is a wariness about the British controversy over EU relations being imported into our arrangements. The issue has torn the UK apart for two years. We want to avoid upsetting something that works for us.”