A scheme apparently being debated by the European Commission suggests the 26-nation passport-free Schengen zone, which does not include the UK, could operate a visa programme similar to the US waiver.

UK passport holders can currently travel throughout member states without having to apply for short-term visas.

But Britain's decision to leave the EU has left question marks over the criteria needed for UK nationals to visit the Schengen zone.

The Guardian reports that the EC is due to unveil new draft legislation later this year as part of a broader response to calls for greater security across the continent following recent terror attacks in France and Belgium.

Camino Mortera-Martinez, a research fellow specialising in justice and home affairs at the Centre for European Reform, was quoted in the newspaper saying: "In theory UK citizens, as third-country nationals, would certainly be subject to the obligations (of such a scheme)."

He added: "This will have to be part of the Brexit talks. It will all have to be negotiated."

Figures released by the Department of Foreign Affairs last month showed a significant rise in the number of passport applications from the UK.

The number of people from Northern Ireland seeking passports increased by 63% in July.

Some 6,638 people in the region applied for Irish passports, compared to 4,070 in the same period last year.

In the first full month since the Brexit result, there were 7,321 applications from people in Great Britain.

The figure represented a 73% increase on July 2015, when 4,242 applications were received.