Wes Streeting has suggested Sir Keir Starmer must go further to undo Brexit – after refusing to rule out that he may run for leadership.
The Health Secretary, 42, previously indicated that the UK could return to the EU customs union and has now piled even more pressure on the Prime Minister.
In recent weeks, the Government said it would remain outside the customs union and single market, with no return to freedom of movement.
Sir Keir has moved closer to the EU already, striking a fresh trade deal with the bloc in May this year that included concessions on red tape and fishing.
But he is still facing more pressure from members of his party, with Mr Streeting suggesting the UK should rejoin the customs union.
The Health Secretary told The Observer: ‘The reason why leaving the EU hit us so hard as a country is because of the enormous economic benefits that came with being in the single market and the customs union.
‘This is a country and a government that wants a closer trading relationship with Europe. The challenge is any economic partnership we have can’t lead to a return to freedom of movement.’
He added: ‘We’ve taken a massive economic hit leaving the European Union. I’m really uncomfortable with the level of taxation in this country.’

Mr Streeting added that the Government has made a ‘good start’ with the revised deal but he would like to see things go further.
He has refused to rule out that he may one day run for rulership, despite last month denying that he was plotting to oust the Prime Minister.
He had been touted as a potential replacement to Sir Keir alongside Home Secretary Shabana Mahmood, who is seen as a rising star in the Labour Party.
Asked whether he was planning a leadership challenge, Wes Streeting previously told Sky News: ‘No, and I think whoever’s been briefing this has been watching too much Celebrity Traitors, and this is just about the worst attack on a faithful I’ve seen since Joe Marler was kicked out and banished in the final.
‘It’s totally self defeating briefing, not least because it’s not true and I don’t understand how anyone thinks it’s helpful to the Prime Minister either.’
Sir Keir is aware of the growing threat to his position and is ‘already fighting the leadership election’ by reaching out to Labour backbenchers, according to The Times.
Angela Rayner has ‘done a deal’ to be Andy Burnham’s running mate if he launches a leadership bid against the Prime Minister, sources claimed this week.
Labour MPs backing Mr Burnham, the mayor of Manchester, said Ms Rayner has agreed to support his bid in return for her old job as Deputy Prime Minister, plus an unspecified senior Cabinet position.
Mr Burnham has been searching for a safe Labour seat in the North to allow him to enter the Commons and challenge Sir Keir.
Last week, The Mail on Sunday reported his Commons allies as saying they have found a seat which is ‘likely to come free’ in the coming months – and which polling suggests that the so-called King Of The North should win.
The seat was not identified, but sources say Mr Burnham has been talking to MPs in safe seats in Liverpool who might be prepared to stand aside, and been keeping a close eye on the Manchester seat held by Andrew Gwynne, who has been suspended from the Labour Party for sending racist and sexist messages. Mr Gwynne has said he does not plan to stand down.
This newspaper has been told Mr Burnham held discussions with Liverpool Walton MP Dan Carden over his seat, which he holds with a 20,245 majority. But sources said yesterday that the talks ‘just didn’t go anywhere’.
Ms Rayner’s backing would be a boost for Mr Burnham as the former Deputy PM – who has not ruled out her own leadership bid – enjoys strong support from Labour members who would vote in the contest.
A Labour MP backing Mr Burnham said: ‘My understanding is that the deal has been done. Angie would go back to being deputy and get a plum Cabinet job.’
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