LONDON — The short and happy life of the United Kingdom Independence Party, or UKIP, may be coming to a close after its only member of Parliament, Douglas Carswell, quit the party on Saturday to become an independent.

Mr. Carswell, 45, was considered a great catch, defecting to UKIP from the Conservative Party in August 2014 because, he said, he believed that the Conservative government was ambivalent about holding a referendum to leave the European Union.

In a message on his website on Saturday, however, Mr. Carswell told his constituents: “Like many of you, I switched to UKIP because I desperately wanted us to leave the E.U. Now we can be certain that that is going to happen, I have decided that I will be leaving UKIP.”

The Conservative government, under Prime Minister Theresa May, is set to invoke Article 50 to carry out Britain’s departure from the European Union, known as Brexit, undermining UKIP’s raison d’être.