Rebel MP Anna Soubry said the last minute change to the wording of the amendment was "unforgivable" and "very disappointing".
Ex-Tory attorney general Dominic Grieve told The Independent UK that he spent the morning negotiating with ministers and agreeing a wording to a new amendment to the legislation.
The Dudley South MP and staunch Brexiteer admitted he was frustrated that MPs were still "quibbling over process issues" which he said meant the European Union had barely had to bother entering into negotiations up to now.
Westminster has argued for continued access, but Brussels maintains third countries can not use the secret signal.Despite threats of British threats to launch its own domestic rival, the European Union has stood firm on its position of no third country access to Galileo's PRS but has said other public uses will continue to be no-limits access for the UK.A British absence from Galileo will, however, significantly hamstring the project, according to a UK Government source familiar with the Brexit negotiations.
The chances of the government being defeated when the Bill returns to the House of Commons later this month has now risen significantly, with trust between May and her MPs at an all-time low.
Tom Tugendhat, Conservative chairman of the United Kingdom parliamentary foreign affairs select committee, said there would be a "new government" if Mrs May lost the so-called "meaningful vote" on the terms of withdrawal, due to take place in October.
Mr Grieve told the Press Association that his comments about collapsing the Government referred to a future vote on rejecting a Brexit deal, not to this week's clash with the PM.
Brexit minister David Davis had earlier warned lawmakers that the government would never allow them to "reverse Brexit" or undermine negotiations.
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Rebels are angry because the Government amendment leaves Parliament facing a "deal or no deal" choice.
He told BBC One's Sunday Politics: 'We could collapse the government'.
Mr Grieve, who had talks on Thursday with ministers, said he could not understand why the change was made.
"We are absolutely confident that we will deliver a Brexit deal that. would be good for the United Kingdom, good for our European friends and partners".
Under these circumstances, a minister must make a statement in Parliament within 14 days and give MPs an opportunity to vote.
"As Parliament gradually assumes a bigger role in the process, the debates have made a "no deal" exit next March less likely and a softer Brexit more likely", Mujtaba Rahman, managing director at Eurasia Group, said in a note.
Theresa May has promised to listen to the concerns of MPs and come up with a solution which "balances" the concerns of Parliament and the wishes of the British public as expressed in the 2016 Leave vote.
The government's prospects of defeat were increased last week when the junior justice minister Philip Lee resigned his post so he could vote against the minister on a meaningful vote.
Shadow Brexit secretary Sir Keir Starmer said: "The Government's amendment is simply not good enough".