Flagship Brexit legislation survived intact as it returned to the Commons despite further Tory concerns and a mini-rebellion.
MPs warned about the potential for ministers to use the European Union (Withdrawal) Bill to sign off changes into law which have an impact on people’s lives without requiring in-depth scrutiny in the Commons.
Senior Conservatives Dominic Grieve and John Penrose welcomed a Government concession but insisted more work is required.
Downing Street announced earlier this week it is to accept an amendment from the cross-party Commons Procedure Committee.
This will create a "sifting committee" involving backbench MPs who will decide whether statutory instruments proposed by ministers require a Commons vote.
Tory former ministers Ken Clarke, Nicky Morgan and Anna Soubry also rebelled to support an amendment pushed by Labour’s Yvette Cooper, which aimed to introduce a "necessity test" to ensure delegated powers included in the Bill should be used "only so far as necessary".
Despite the Tory support, Ms Cooper’s proposal - amendment 49 - was defeated by 312 votes to 295 - majority 17.
This was the smallest majority in the five votes won by the Government as the Bill remained unchanged following the sixth day of committee stage.
Labour was accused by Liberal Democrat leader Vince Cable of supporting an "extreme" Brexit after the Opposition frontbench abstained on a vote linked to the single market.
Lib Dem former minister Tom Brake’s amendment 124, which aimed to prevent the Bill’s regulation-making powers being used to "create barriers" to the UK’s continued membership of the single market, was defeated by 315 votes to 93 - majority 222.
Mr Clarke and Ms Soubry also rebelled to support Mr Brake’s amendment. They were joined by 44 Labour MPs.
Debate on committee stage day six focused on clause seven of the Bill, in which the Government asks Parliament to delegate legislative power to change the statute book so retained EU law functions effectively after Brexit.
Former minister Mr Penrose said: "As it stands at the moment I don’t think that the words that they have got in this Bill is passing the sniff test for an awful lot of us in this room.
"I am extremely pleased to see therefore the open and positive and constructive way that ministers have been approaching this issue and the commitment from the despatch box this afternoon to go back and have a further look at it.
"I couldn’t tempt the minister into a firm promise to introduce an amendment, but I think that is going to be what is necessary by the time we get to a report if it is going to be amended in a way which does become acceptable and passes the sniff test."
Former attorney general Mr Grieve accepted the "sifting committee" would improve the scrutiny process, providing it had the right MPs to navigate through the "avalanche" of statutory instruments.
He also said he was putting ministers "on notice" over the Bill’s so-called Henry VIII powers - a term reserved for measures which allow reforms with little parliamentary scrutiny - adding there could be amendments re-tabled at report stage.
Mr Grieve told the Commons: "The Government has got to come up with a response as to how it can constrain the powers that are set out.
"At the moment, my own opinion is that these powers are far too stark and far too great and are not necessary."
Amendments - including the "sifting committee" proposal - tabled by Tory MP Charles Walker on behalf of the Procedure Committee were debated during committee stage day six on Tuesday but cannot be voted on until Wednesday.
Responding for the Government, Brexit minister Steve Baker said the Bill was not an attempt to create "a power for ministers to change law simply because they don’t like it".
Mr Baker said that the aim of clause seven was to take the "minimum powers necessary" to "deliver a working statute book on exit day".
He told Tory backbenchers that the Government had listened "extremely carefully" to their concerns over the so-called Henry VIII powers, adding he was "willing" to work with Mr Grieve and others ahead of the Bill’s report stage.
Mr Baker also said any major policy change would come through primary legislation, though small policy choices may be made through secondary legislation.