LONDON — Boris Johnson has been British prime minister for barely a week, and the honeymoon appears to be over. His Conservative Party lost a special election, cutting his working majority in Parliament to just one seat at a critical moment for the country.

The narrow defeat in a previously Conservative-held district, the Brecon and Radnorshire area of Wales, was a brutal reminder of Mr. Johnson’s weakness in Parliament.

It immediately fueled speculation that Mr. Johnson would seek to increase his majority by holding a general election sooner rather than later. The only question is whether it would be before or after Oct. 31, the deadline for the country to leave the European Union.

“The election campaign is effectively already underway,” said Anand Menon, professor of European politics and foreign affairs at King’s College London.