LONDON—British Home Secretary Amber Rudd said the U.K. would be ready to respond to the attempted murder of a Russian double agent living in Britain if it was attributed to Moscow, describing the use of a nerve agent on U.K. soil as a “brazen and reckless act.”

“There is nothing soft about the U.K.’s response to any sort of state activity in this country,” Ms. Rudd told the British Broadcasting Corp. Thursday. “You may not hear about it all, but when we do see that there is action to be taken, we will take it.” She didn’t...