LONDON—U.K. Conservative Party leader David Cameron faces an intense round of political jockeying to gain control of the British government, as his party apparently won more House of Commons seats than rivals, but fell short of a majority. Early projections showed Mr. Cameron's party won 305 seats, short of the 326 seats required for a majority but more than the 255 seats for Labour and 61 seats for the Liberal Democrats, according to exit polls. However, exit polls can be wildly off and even small margins of error could produce very different final outcomes. If the final results confirm that...