MPs should vote on the terms of Brexit negotiations, Labour's shadow Brexit secretary Sir Keir Starmer has said.
Sir Keir told the BBC the referendum result "has to be accepted" but accused the PM of trying to "manoeuvre without any scrutiny" on how to achieve it.
He also said he believed immigration should be reduced, by increasing British workers' skills.
Downing Street said his call for a vote was "an attempt to find another way to thwart the will of the British people."
The government intends to trigger Article 50, the official process for exiting the EU, by the end of March 2017.
'Axe to economy'
At the Conservative Party conference, Prime Minister Theresa May said the government would strike a deal with the EU as a "sovereign, independent" UK, but her speech has raised concerns among some that the UK is headed for a "hard Brexit" - without unfettered access to the single market.
Sir Keir, who returned to Labour's front bench last week in a reshuffle following Jeremy Corbyn's re-election as Labour leader, told BBC One's Andrew Marr Show: "The referendum is clear and has to be accepted and we can't have a re-run of the question that was put to the country earlier this year.
"But, and it's a big but, there has to be democratic grip of the process and, at the moment, what the prime minister's trying to do is to manoeuvre without any scrutiny in Parliament and that's why the terms on, which we're going to negotiate absolutely have to be put to a vote in the House."
By Tom Barton, political correspondent
Jeremy Corbyn is "not concerned" about immigration - that's the official line from his office.
And Diane Abbott, who Mr Corbyn promoted to shadow home secretary just a few days ago, has said that people who complain about immigration want to see fewer "foreign-looking people on their streets".
Yet shadow Brexit secretary Sir Keir Starmer, who has also been in the job just a matter of days, says "people are understandably concerned" about immigration and that he thinks "it should be reduced".
It's early days for Mr Corbyn's new shadow cabinet - but already some cracks are beginning to show.
He said no-one voted "to take an axe to the economy" and Mrs May's "stance on the single market is making it nigh-on impossible" for Britain to have access to it which posed a "huge risk".
Sir Keir also told the BBC "palpable and clear" concern about immigration had to listened to. Asked if he thought it was too high or low, he replied: "I think it should be reduced, and it should be reduced by making sure we've got the skills in this country that are needed for the jobs that need to be done. "
Labour leader Jeremy Corbyn has said he will not "sow division" by pledging to cut immigration - his spokesman said at the time of the Labour conference he was "not concerned about numbers".
The interview follows reports of a cross-party move involving former Labour leader Ed Miliband and former Lib Dem leader Nick Clegg to seek a stronger role for the Commons on Brexit.
In an article in the Observer, Mr Miliband said: "There is no mandate for hard Brexit, and I don't believe there is a majority in parliament for it either... it has to be a matter for MPs." Mr Clegg told the same paper it was not "remotely acceptable" to leave it to the government to decide the terms.
But a Downing Street source said: "While Labour are looking for ways to stop Brexit we are focused on making a success of it. Of course Parliament will have a role in the exit process, but this suggestion is simply an attempt to find another way to thwart the will of the British people."
Conservative MP and former cabinet minister Iain Duncan Smith told the BBC's Sunday Politics that it was "pretty clear" that the UK would not remain a member of the single market once it left the European Union.
"I think, when you add all these things together it becomes, I believe, pretty clear really that … there is no way really that the European Union will be able to allow us to be a member of the single market. Which by the way is not the same as access."
The prime minister has said that immigration controls are a post-Brexit priority, but other EU leaders have said that would be incompatible with the UK remaining in the single market.
It has been reported that Mrs May is against holding a Parliamentary vote on the process. She has said MPs should be informed "at various stages" but told the BBC last week the government had to be able to negotiate but be sure that "we don't set out all the cards in our negotiation."