The bombshell survey shows that fewer than half of voters in Norway and Switzerland – two countries seen as potential models for Brexit Britain – see the bloc in a positive light.
However, in stark contrast the EU enjoys an overwhelmingly favourable reputation in countries including China, India and the United States where it is seen as a global force for good.
The results appear to quash claims by some politicians, especially Norwegian leaders, that people in the UK would “hate” being outside the club and are instead far better off in it.
On the contrary, there appears to be very little appetite to sign up for full membership within the four Efta states – Norway, Iceland, Switzerland and Liechtenstein – which are all part of the Single Market.
Before the referendum Oslo’s leader Erna Solberg warned the UK not to vote to quit the full EU project and revert to simple economic ties, telling voters “you will hate it”.
The main argument against what has become known as the Norway model is that countries participating in the European Economic Area (EEA) have to pay budget contributions and accept its rules, but get no say over them.
But in reality EU laws are drawn up at a technical level – where the Efta states are represented – before simply being signed off by leaders and ministers at meetings of the European Council.
And it has been calculated that the EEA states, which have their own independent court, only have to implement less than a third of ECJ caselaw relating overwhelmingly to economic matters like common standards.
According to the Eurobarometer results just 43 to 46 per cent of Norwegians and Swiss view the EU positively despite the fact they are the two countries with the closest ties to the bloc.
Brussels also has an unsurprisingly bad image in Russia and Turkey – two countries it is at loggerheads with – but even there around half of people think it is a positive influence overall.
And elsewhere in the world, far from the many crises which have plagued its recent history, the project still enjoys a formidable reputation as a bastion of trade and prosperity.
An astonishing 94 per cent of Brazilians view the bloc positively, compared with 84 per cent in China, 83 per cent in India, 79 per cent in Canada, 76 per cent in Japan, 75 per cent in the US and 67 per cent in Australia.
The results back up comments made by the EU Commission president Jean-Claude Juncker, who has previously said people in the rest of the world are…