The shadow foreign secretary insisted Jeremy Corbyn’s party are not “sweeping any options off the table” when she was asked about their stance for Britain’s European divorce.
Labour has been riddled with mixed messages with Mr Corbyn, John McDonnell and Barry Gardiner all delivering contrasting visions for Brexit.
Appearing on BBC Radio 4’s Westminster Hour, Ms Thornberry was asked to clarify their position for the programme’s listeners.
She said: “Our position is we need to be able to negotiate a new relationship with the European Union – we’re not sweeping any options off the table.
“Some of the people who have been making a contribution to the debate, their contribution is greatly welcomed but, with respect to them, they are not the ones leading the party on this.”
Ms Thornberry added: “What we need to do is not fixate on forms, what we need to fixate on what the end result will be – how do we best look after our economy and the safety and security of our citizens.”
Mr Gardiner, the shadow international trade secretary, said staying in the customs union would be a “disaster”, while Mr Corbyn hinted he believes Britain must be out of the EU’s single market.
The Labour leader told the BBC’s Andrew Marr: “The single market is dependent on membership of the EU.
“What we’ve said all along is that we want a tariff free trade access to the European market and a partnership with Europe in the future.”
Mr Corbyn revealed he would instead push for tariff free trade access to the market rather than membership.
“The two things are inextricably linked,” he said.
“So the question is the kind of trade relationship in the future and we’ve made it very clear we want tariff free trade access with the European market.”
Prime Minister Theresa May has, however, fired warning shots at any attempts for a soft Brexit from her own Cabinet or Labour.
A spokesman for Mrs May declared free movement of EU citizens will definitely end after Britain cuts itself free from the Brussels bloc in 2019.
He said it would be “wrong to suggest” freedom of movement would continue unchanged.
Chancellor Philip Hammond’s desired “off-the-shelf” transitional solution was also rubbished.
Mrs May’s spokesman said: “Free movement will end in March 2019. We’ve published proposals on citizens’ rights. Last week, the Home Secretary said there would be a registration system for EU national arriving post-March 2019.
“Other elements of the…