That will not be easy. The seven rebel lawmakers will sit as independents in Parliament, having decided not to establish a new political party, at least for now. Doing so is difficult in Britain because the country’s electoral system makes it hard for smaller groups to win representation in Parliament. A faction that splintered from Labour in the 1980s to form a centrist social democratic party ultimately failed.

Nevertheless, in some parts of Europe, new political forces have exploited the weakness of existing parties, including in France where President Emmanuel Macron successfully created a new centrist movement.

In Britain, Mr. Travers noted, there is “a gaping gap” in politics. Under Mr. Corbyn, Labour has both its most left-wing leader in decades and a lifelong critic of the European Union, who has resisted demands from some of his lawmakers and party members to support another referendum on Brexit.

The Conservatives have their schisms as well. Within the governing Conservative Party of Prime Minister Theresa May, Brexit has been embraced with enthusiasm by party activists, who tend to be older and more nativist. This has strengthened the hand of hard-liners, including lawmakers who meet as the European Research Group, some of whom are happy to contemplate leaving the European Union without any agreement.

That has left the party’s more pragmatic lawmakers on the defensive, confronting the prospect of something they fear could be an economic catastrophe. Several of the more pro-European Conservative lawmakers have been threatened with deselection by their local parties, a development that mirrors the faction-fighting within Labour.

While there is a vacant space at the center of Britain’s politics, the middle-of-the-road Liberal Democrats have failed to recover the credibility they lost with voters during their coalition government with the Conservatives from 2010 to 2015.

On Monday, the seven lawmakers gave differing reasons for their resignations when they addressed the media. Luciana Berger, who represents Liverpool Wavertree, has been a vocal critic of Mr. Corbyn’s handling of anti-Semitism allegations, and was threatened with a vote of no-confidence by local party activists, a motion that was eventually withdrawn.