The seven MPs who broke away from the UK's main opposition Labour Party took their seats as an independent group in parliament for the first time on Tuesday as rumours swirled of possible further defections.

The biggest split in British politics in nearly four decades showed up divisions in both Labour and the ruling Conservatives that have been stretched to breaking point since the Brexit referendum in 2016.

One of the seven lawmakers, Chuka Umunna, a leading campaigner for a second referendum, said on Tuesday that he now wanted to establish a new centrist political party by the end of the year at the latest.

"There needs to be an alternative," he told BBC radio.

The MPs said they were leaving the party over leader Jeremy Corbyn's support for Brexit and his failure to stamp out anti-Semitism.

Left-wingers were divided over the creation of the "Independent Group", pointing to the ultimate failure of the Social Democratic Party started by four rebels from the Labour Party in 1981.

"During a national crisis over Brexit, the breakaway of seven MPs with no policy programme is a dangerous distraction," wrote Guardian columnist Polly Toynbee, who once supported the SDP.

But Labour's deputy leader Tom Watson said his party had to change or it could "see more days like this".

"I love this party but sometimes I no longer recognise it," he said in a video statement.

The BBC reported that two Conservative MPs could switch to the new group and other media reported more Labour MPs could split.

Conservative MPs Sarah Wollaston, a pro-EU moderate whose name has been mentioned in the media as a potential defector, tweeted that Brexit hardliners were "taking over the Tory party".

"Soon there will be nothing left at all to appeal to moderate centre ground voters," she said.

Media reports noted that fellow Conservative Anna Soubry removed references to the Conservative Party on her Twitter biography.

But Conservative MP Kwasi Kwarteng told a Brexit conference on Tuesday he was "not sure" that any Conservatives would join the group.

"If they do, I think that would be very regrettable," he said.

Nigel Farage, whose UK Independence Party played a huge role in bringing about the Brexit vote, told the same conference that the breakaway signalled a "reshaping of British politics".

"The existing two and a half party system just can't cope with Brexit. I do begin to think that maybe what we saw yesterday was a beginning of a fragmentation of our establishment parties," he said. 

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