Britain did hold elections during WWII. In 1945 they held an election that resulted in Clement Attlee being elected Prime Minister, replacing Churchill. There were also numerous elections to fill in empty seats in parliament during the war.
In Britain each sitting of parliament can last for 5 years at most before an election needs to take place. Parliament can be dissolved and elections called for earlier then every 5 years, but 5 years is the max. Parliament extended this 5 year limit during the war however.
