A former shadow minister has said Labour must have “clear red water” between itself and the Conservatives on Brexit, as he criticised the party’s position on leaving the EU.

Chuka Umunna said Labour should back Britain staying in the European single market and customs union, adding that it was not enough to have an end goal of not damaging the economy.

The former shadow business secretary also told the BBC he was not opposed in principle to a second EU referendum, if the UK could not negotiate the kind of Brexit voters were promised during last year’s campaign.

Umunna has been a consistent advocate of the UK staying in the single market and customs union, voting against his party on the issue earlier this year alongside dozens of other Labour MPs.

“There’s got to be clear red water between our position, the Labour party’s position, and Theresa May’s extreme, jobs-destroying Brexit position,” he told BBC Radio 4’s Today programme.

“To my mind, that means we absolutely do need to be arguing for the UK to remain a member of the single market and also of the customs union after we leave the European Union.”

Umunna, a leading supporter of the Open Britain campaign group, said Labour’s aim was to have a future relationship with the EU that put jobs first and did not damage the economy.

“The argument is that the institutional arrangements aren’t the big issue here – it’s the goal,” he added. “The problem is the means of withdrawing from the European Union and the institutional arrangements that you have of course shape those ends and goals that you wish to achieve.

“That’s why not just the TUC, not just Labour party members but business too, there is a broad consensus that we should, at least in the medium term, be seeking to stay in the customs union and the single market, but also that would be the preferable option in the long term.”

Umunna went on to say that as negotiations progressed, people were beginning to see that “it is impossible to deliver the things that people thought they would get”.

Asked about the potential for a second referendum, he said: “I’m not opposed in principle to that, but I think what the British people expect us to do is to do our very best to deliver Brexit in the terms they thought that they could have. And if we’ve exhausted all the avenues through this negotiation, then I think it’s an open question on that.

“But at the moment our instruction is get the very best deal for the United Kingdom in the way that we thought you would be delivering for us.

“So far the government, not just because they’re incompetent but because it’s proving to be impossible, is not able to achieve these things.”