When standing for election a politician will usually run as the member of a political party. The quid-pro-quo of this arrangement is that the party will collectively campaign for all their candidates. In return, the party will expect the successfully elected MPs to support their leader's policies and support that leader in any votes-of-confidence.
Occasionally, an MP will decide to leave their party. This is often called “Crossing The Floor” for rather archaic reasons. Sometimes that MP becomes independent, sometimes they join other parties. Most famously, wartime leader Winston Churchill left the Conservative Party in 1904 to join the Liberal Party, only to return in 1924.
When an MP does this, it will often be met with calls for that MP to put themselves up for re-election by their voters in a by-election. Normally, this only happens when an MP dies, resigns, or maybe appointed to the House of Lords.
“The voters elected a Conservative to be their MP, not a Liberal! You should let the voters have their say if they want to keep you as their MP.”