The 90-year-old Carry On star is being treated by specialists after falling ill on a bus ride in London.
Leslie, who voiced The Sorting Hat in the Harry Potter films, was with his wife of nine months, Zara, at the time.
"Leslie is very strong and I’m sure he will pull through," she said. "I love him to bits and I know his millions of fans will want to wish him well for the future.
"Leslie suddenly started leaning on me and was unable to put a ticket in his coat pocket," she added. "He had terrible pains in his left arm so I stopped the bus and called an ambulance which took him to University College Hospital in Euston.
"He kept saying to me 'don’t cause a fuss' but I knew he was unwell and needed urgent medical help. From there, he was then transferred to a top neurosurgery hospital in the capital."