By Elizabeth Piper, Alistair Smout and Andrew MacAskill LONDON (Reuters) -Eight Conservatives will fight it out to succeed Boris Johnson as party leader and British prime minister after winning enough nominations from their colleagues to go through to the first round of voting on Wednesday. Only two hopefuls failed to secure the 20 necessary nominations, leaving a wide field of candidates seeking to win the backing of the party with promises of tax cuts, honesty and serious government – a contrast to Johnson who was forced to announce he would resign after a series of scandals. Former finance …