Yvette Cooper alleged that the prime minister was cutting out the home secretary over immigration.
It comes after Braverman – who was re-appointed home secretary by Sunak just six days after she was forced to quit for breaking the ministerial code – was criticised for her handling of the migrant crisis.
Shadow home secretary Cooper went on to say the home office was in “total chaos” and that the Tories only provided “rhetoric” not “practical plans”.
However, a source close to Braverman hit back, telling HuffPost UK: “Laughable nonsense and a desperate line of attack which says more about the person making it than anything else.”
Labour has pledged to introduce a new fast-tracking process for migrants from “safe” countries to clear the backlog of asylum claims.
Cooper told Times Radio: “This idea that [Sunak] has appointed a home secretary Suella Braverman six days after she was sacked for security lapses – he reappointed her and now he’s sidelined her and he’s obviously excluding her from the decisions.
“So that in itself is chaotic. If you’ve got Suella Braverman saying one thing, you’ve got Robert Jenrick [the immigration minister] saying another, you’ve got Rishi Sunak saying something else entirely.
“We’ve had eight immigration ministers and six home secretaries in the last seven years alone.
“That’s what the Conservatives have done in the way that they have been treating this. We just get rhetoric from them. We don’t get practical plans.”
Labour cited home office figures showing that, of 7,000 Albanians who made asylum claims after travelling to the UK on a small boat in the year to June, fewer than 1% have had their case determined.
Cooper called on the government to immediately introduce fast-tracking for Albania and those from other safe countries “so that unfounded asylum claims can be rejected and returned in a matter of weeks”.
Labour points to similar systems in use in Sweden and other European countries, claiming that such an approach would be implemented straight away and avoid the need to pass legislation or lengthy legal delays.
The last time Labour was in government it introduced a system that fast-tracked asylum claims believed to be manifestly unfounded, with decisions made within seven to 10 days.
Labour said their fast-tracking scheme would allow the government to focus on asylum seekers who have fled persecution, while also saving taxpayers’ money on hotel accommodation.
However, the government is also said to be reviewing plans to fast-track the removal of asylum seekers from designated “safe” countries, a list that would include Albania.
According to The Times, the home secretary is drawing up legislation to make it easier to reject and remove asylum seekers from Albania.
Under the proposed changes, claims would be automatically refused and remove a check officials are currently expected to carry out.
The move is designed to target Albanians after more than 12,000 arrived from the Balkan country via small boats this year – about a quarter of all Channel crossings.