Attendees at the party’s annual conference have been buoyed: both by leader Kemi Badenoch’s rising poll ratings and by a mock Bayeux Tapestry. But the challenge from Reform U.K. remains.

A new political party called Restore Britain is threatening the rise of Nigel Farage's hard-right group, with a tougher anti-immigrant stance and the backing of tech trillionaire Elon Musk. Led by ...