MOSCOW—Two Russians charged by the U.K. with attempting to murder a former Russian spy acknowledged they were in the English city he called home on the day of the poisoning—but said they were there as tourists to admire sites including the 123-meter spire of its world-famous cathedral.

The claims by the two men, who said their names were Alexander Petrov and Ruslan Boshirov, contradict the case presented last week by the British authorities, who identified them as would-be killers for Russian military intelligence and said...