KYIV, Aug. 25 -- The missiles that have already reached deep into Russian-held territory will soon be built in Ukraine itself, if Andy Burnham can persuade Washington to let him share what London knows.

Britain's Prime Minister arrived in Kyiv on Monday to mark Ukraine's 35th Independence Day, making it his first foreign visit since taking office. He did not come empty-handed. Burnham announced that the United Kingdom would share classified technical information enabling Ukraine to manufacture Storm Shadow cruise missiles on its own soil, a step no British government had previously been prepared to take and one that the United States has declined to match with its own weapons technology.

The Storm Shadow is a precision strike weapon wit...