A prominent Remain campaigner has said he is thinking of applying to head the Government’s new Brexit Opportunities Unit as it would offer the chance to rejoin the EU.

Making the tongue-in-cheek pitch at Westminster for the director post, Lord Adonis argued it was “such an exciting opportunity” that he was prepared to do the job, which is offering a salary of up to £120,000, for nothing.

The Labour peer and staunch critic of leaving the bloc said reapplying to be part of the single market and customs union would eliminate trade barriers and allow Britons to move freely across the EU and “not be locked up in Boris Johnson’s Brexit Britain”.

Thanking him for his job application, Brexit minister Lord Frost said it was “very open” to Lord Adonis to apply, although he disagreed with his assessment.

The Tory frontbencher, who negotiated Britain’s trade deal with the EU, argued that Brexit “will be hugely in the interests of everybody in this country”.

The exchange in Parliament came with moves under way to recruit a director of the Brexit Opportunities Unit, which aims to build on the UK’s new freedoms following its break from Brussels and help make the most of the potential economic and political gains.

The closing date for applications is July 25 with interviews planned for September.

Lord Frost told peers the job would fetch a salary of up to £120,000, which was “appropriate for the calibre of candidate that the role requires”.

He added: “The director of the unit will of course lead an ambitious programme of reform and address many of the most important questions facing the UK.”

Pressing the minister, Lord Adonis said: “I’m thinking of applying for this job.

“It’s such an exciting opportunity that I would be prepared to do it for nothing.

“I was wondering what the minister might think about my application?

“Can I give him my pitch for the job, which is that the biggest opportunity for the director of the Brexit Opportunities Unit is the opportunity to reapply to join the single market and the customs union?

“So that we eliminate trade barriers with the European Union, we eliminate the need for any trade barriers north-south or east-west in respect of Northern Ireland, and we extend once again to the British people the great opportunity to be able to travel, study, work, settle, live and form relationships across the whole of the continent and not be locked up in Boris Johnson’s Brexit Britain.

“Does he find that an exciting prospectus?”

Responding, Lord Frost said: “I thank him for his job application.

“Of course it is very open to him to apply if he wishes.

“It won’t be for me to judge whether he meets all the criteria for that job or not.

“It won’t surprise you to know that I disagree with his assessment of where we stand as a country.

“Brexit will be hugely in the interests of everybody in this country as we take forward the exciting opportunities to reform our own rules, take back control of our own legislation and run our own country as we wish.”

Highlighting the examples of a new points-based immigration system and steps to agree free trade agreements with countries around the world post-Brexit, Lord Frost said: “There is a long list of opportunities that we will be able to take advantage of.”