A Pentagon spokesman said on Thursday that the US believes the use of the missiles would be an “escalation”, and provoke a response by Russia against Ukraine’s Western allies.
Mr Zelensky’s criticism of the UK comes after Sir Keir suggested at last month’s Nato summit that Ukraine would be allowed to use the missiles.
A Downing Street spokesman later said the ban using Storm Shadows inside Russia, first imposed by the previous Conservative government, would remain.
A Ministry of Defence spokesman said on Sunday that there had been “no change in the UK’s position”.
However, four former Tory defence secretaries told The Telegraph Sir Keir should do more to help Ukraine, after John Healey, his Defence Secretary, said Britain’s support would be “iron clad” under Labour.
Sir Michael Fallon, who served as defence secretary under Theresa May’s government, said: “It can’t be right to let Putin hit a children’s hospital with glide bombs from miles over the border, yet bar Ukraine from defending itself with long-range missiles like Storm Shadow.”
Sir Ben Wallace, who served under Boris Johnson, said: “Time and time again those that want to do nothing have used the ‘escalation’ excuse.
“They used it before the conflict, they used it when we supplied short-range anti-tank missiles, they used it when we supplied tanks.
“The reality is it is the appeasers that use this language and all the while Ukrainians suffer. Storm Shadows have been making a real difference in Crimea, which Russia already believes to be sovereign Russian territory, without escalation.”