Less than two hours after his government's Brexit plan suffered a crushing defeat in Parliament, U.K. Chancellor of the Exchequer Philip Hammond jumped on the phone. On the other end of the line: executives and business lobbyists alarmed by the prospect of Britain crashing out of the European Union (EU) without a deal.

During the hour-long conference call with the country's top business groups and executives—from companies including Amazon.com Inc., Siemens AG, and Airbus SE—Hammond sought to soothe frayed nerves, assuring them that Parliament is working to avoid a chaotic exit and floating the prospect of a delay to the end-of-March departure date.

He was met with another outpouring of disappointment and concern from corporate leaders. Several have decided to ramp up contingency planning, even as Prime Minister Theresa May pledges cross-party talks to break the impasse.