A broker looks at a graph on his computer screen on the dealing floor at ICAP in London, Britain January 3, 2018.
She said she had been told by a source that either Theresa May "dumps" the plan signed off at Chequers or "another minister will go, then another, then another, then another".
"Investors believe she will keep hold of the reins", London Capital Group analyst Jasper Lawler said.
At the meeting, May pressed Davis and other government officials to back her plan for maintaining close trade ties with the EU, Reuters reported.
Johnson's resignation marks a major blow to the stability of May's government, with speculation it could collapse already rife.
Less than nine months remain until Britain leaves the bloc on March 29, 2019.
David Davis has threatened to resign on a number of occasions as Brexit Secretary.
UK Brexit ministers Davis and Baker quit in major blow to May
Environment Secretary Michael Gove said Sunday that it did not contain everything he wanted but "I'm a realist". The resignation is a blow to Mrs May as she seeks to win over Eurosceptic MPs to her proposed Brexit vision.
Some Brexit-supporting legislators are angry at the proposals, saying they will keep Britain tethered to the bloc and unable to change its rules to strike new trade deals around the world.
Davis was particularly critical of the proposal for a "common rulebook" to allow free trade in goods, saying this "hands control of large swathes of our economy to the European Union and is certainly not returning control of our laws in any real sense".
Conservative MP Jacob Rees-Mogg, a leader of the party's "hard Brexit" faction, compared May's plan to an egg so softly boiled that it "isn't boiled at all".
"The mess caused by Brexit is the biggest problem in the history of EU-UK relations and it is still very far from being resolved, with or without Mr Davis", he said.
"I do not agree with your characterisation of the policy we agreed", she said, asserting that it "will undoubtedly mean the returning of powers from Brussels to the United Kingdom".
"This afternoon, the Prime Minister accepted the resignation of Boris Johnson as foreign secretary", a Downing Street spokesman said.
Davis's resignation could embolden Brexit-supporting Conservative parliamentarians to challenge May's leadership. But some senior pro-Brexit ministers have backed May's plan.
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