A senior lawmaker in Britain's main opposition Labour party has ruled out that its leadership will definitively pursue a second Brexit referendum vote as its next course of action.

The comments follow Parliament's outright rejection in a vote Wednesday night of Labour's alternative Brexit proposal, which included a permanent membership of the EU's customs union.

Emily Thornberry, the shadow foreign secretary and therefore the Labour party's chief foreign affairs spokesperson, acknowledged the party's latest legislative defeat, but insisted that Labour's preference for a Brexit that involves close alignment with Europe on trade remained a viable parliamentary option for the future.

"There may be other opportunities for us to put it again," she told CNBC of the proposal, "because we don't know what's going to happen in the next few days."

Thornberry criticized the current version of a deal with the European Union, negotiated by Prime Minister Theresa May and her Conservative — or as it is often known, "Tory" — government. And she described the uncertainty surrounding the approval process for the "lousy Tory deal" as being "quite scary," and she insisted that as a consequence the British public should have a say over its eventual passage into law.