A powerful cross-party group of MPs is to renew pressure on ministers over Brexit by forcing a parliamentary vote on whether they should reveal their plans for the UK’s future outside the EU before negotiations begin. In a further sign that cross-party alliances are forming in favour of a soft Brexit, former party leaders Ed Miliband and Nick Clegg will join forces with the shadow Brexit minister, Keir Starmer, and the former Tory minister Nick Herbert to demand a Commons debate this week.

The motion they will table will call on the government to release a substantive outline of its plan – including its broad intention for the UK’s future relationship with the single market – and ensure that parliament can amend its contents before exit talks start early next year.

The move is aimed at preventing a hard Brexit, under which the UK would retain no ties with the EU’s single market, and ensuring that MPs are not sidelined in the plans for exiting the EU.

A new poll exclusively revealed to the Observer shows a clear majority of the British public supporting continued membership of the single market, despite the narrow 23 June vote to leave the EU. Of those surveyed in a poll commissioned by Open Britain, the successor to Britain Stronger in Europe, 59% of people wanted to stay in the single market, while 41% wanted to leave.

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At the recent Tory party conference, Conservative ministers suggested that the UK would be taken out of the single market if that was the only way they would be able to win back control of the UK’s borders and control immigration.

While the survey shows remain voters overwhelmingly support staying in the single market, leave voters are divided, with 45% believing the UK should leave the single market, 28% saying it should stay in, and 26% not sure.

Alarmingly for ministers leading the push for hard Brexit, a majority of all voters believe such an approach would leave Britain worse off. Of them, 58% say leaving the single market would have a negative impact on the economy, while 32% believe the country would fare better outside the single market and 12% do not think leaving would make any difference.

Pressing the government to allow a vote in parliament on its intentions, Starmer said: “The government has now finally conceded that there needs to be proper scrutiny of its plans for Brexit. That is a real victory for parliament. Now it needs to take the next step and guarantee the House of Commons will have a chance to vote on the basic terms of Brexit before article 50 is invoked. Anything less would be sidelining parliament on the defining issue facing Britain.”

Clegg, speaking on behalf of the Open Britain campaign, said: “The government should not take decisions that will have massive consequences, like leaving the single market, without seeking parliament’s approval. David Davis [the Brexit secretary] previously advocated a pre-negotiating white paper and has always championed parliamentary sovereignty. The government must now respect that by committing to a debate and a vote in parliament on its negotiating position.”

Former police minister Herbert added that the cross-party group was not seeking to “delay or frustrate the referendum decision”, but wanted to prevent “hard Brexit ideologues” from damaging the country by pulling out of the single market without proper scrutiny.

A majority of Conservative, Labour and Liberal Democrat voters support continued membership of the single market, with only Ukip supporters backing the alternative, suggesting that Theresa May’s calls for a hard Brexit have yet to resonate with voters.