Owen Smith has raised the possibility of a future Labour government seeking renewed British membership of the EU, saying the UK could rejoin the bloc if the political and economic cost of Brexit was seen as too high.

The Labour leadership challenger has previously promised to push for a new referendum on the terms of any Brexit deal if he defeats Jeremy Corbyn, but on Sunday went further.

He said it would be “sensible and responsible” for a Labour government to seek a return to the EU, if Theresa May led the UK out of the union before the 2020 election, and if the provision of public services was badly hit by the move.

Labour leadership: Jeremy Corbyn v Owen Smith on BBC Question Time

Asked on BBC1’s The Andrew Marr Show about the possible fallout from the government triggering article 50 in time for an exit before the next general election, Smith said reapplying for membership again was theoretically possible.

“I think it’s very hard to answer because it’s a hypothetical question,” Smith said.

“At that point, if we had gone into a further recession, if we had the prospect of another 10 years of Tory austerity, if they were saying that the price for our staying out is opening up the NHS to private sector competition, it is worse terms and conditions – ‘more flexibility and less red tape’, as the Tories would no doubt dub it – then I think the sensible and responsible thing for a Labour government to do is to say we are better off in the European Union.”

Asked if this could potentially mean Britain being obliged, as a new member, to sign up to the Schengen free-travel area, Smith said: “Potentially, but again we are getting into hypotheticals built on hypotheticals.”

The former shadow pensions secretary argued that, rather than reach this point, May needed to give Britons a say on what an eventual Brexit deal would mean. “If she were to trigger article 50 before the British public knows what the real Brexit deal is, I think that would be dereliction of duty on her part,” Smith said.

“My point is simple: once we know what the deal is, that’s the point at which you have an extra democratic moment in Britain.”

This could involve another referendum, or a general election, with Labour arguing for remaining in the EU “because the terms of the deal are not what we were promised”, Smith said.

Corbyn has ruled out pushing for a second referendum on Brexit, arguing that the 23 June result must be respected.

Corbyn’s leadership team pointed out on Sunday that Tim Roache, general secretary of the Smith-supporting GMB union, also did not agree with Smith about this, telling Sky News’s Murnaghan programme “that boat has sailed”.

A spokesman for Corbyn’s leadership campaign said of Smith: “He has made a second referendum on the EU a core part of his campaign and today one of his chief backers has rejected the policy. If he can’t even unite his own supporters, how can he unite our party?”

Smith is seen as unlikely to defeat Corbyn in the vote of Labour members and registered supporters, to be announced at the start of the party’s annual conference on 24 September.

Smith remains publicly bullish, however. Asked by Marr how confident he was of success on a scale of one to 10, Smith said: “Ten, absolutely.”

This article was written by Peter Walker Political correspondent, for theguardian.com on Sunday 11th September 2016 14.41 Europe/London

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