"Ensuring that the financial services sector can attract the talent it needs to thrive is also vital as we leave the EU", Davis said.
Labour MP Chuka Umunna, co-chair of the cross-party parliamentary group on European Union relations, said the move was "totally insufficient" and gave "no guarantee of a meaningful vote".
Later, on the first day of the bill's committee stage in the House of Commons, the Government also comprehensively won a vote (318-68) on the bill's provision for the 1972 European Communities Act to be repealed on exit day.
But his sop failed to win over most MPs, who feel it would be a hollow vote as they would be given a take it or leave it scenario just days before Brexit and demanded that Parliament be given a vote on the final Brexit deal much earlier.
The government said it wants an implementation period of around two years after Brexit to stop an economically damaging "cliff-edge" - but insists Britain will be fully out of the EU.
"Parliament could do nothing at all to shape the nature of that withdrawal agreement".
Brexit Secretary David Davis unveiled plans for the UK's divorce deal to be written into law, meaning both MPs and peers will be afforded a vote on the agreement between London and Brussels.
Reacting to the Brexit Secretary's announcement, Ms Allen tweeted: "Pointless if we have enshrined a drop dead date in the Bill, & get a deal at 11th hour!"
And he said there would be no withdrawal agreement bill, or vote, if London can not strike a deal with Brussels.
Antoinette Sandbach told the Press Association: "The announcement is meaningless if, for any reason, the timetable slips beyond March 2019".
He said the bill must be amended "to provide for a proper, not a fake, meaningful vote before any exit day".
Meanwhile, former Tory constitution minister John Penrose welcomed the Government's stronger pledge on a parliamentary vote, but expressed continuing concerns over the use of so-called "Henry VIII powers" as provided by the EU Withdrawal Bill.
Keir Starmer, Labour's chief Brexit spokesman, said the proposal was "a significant climbdown from a weak government on the verge of defeat".