The Short Version
The claim is true. Multiple independent climate databases consistently report Milan's average annual rainfall at approximately 943–945 mm, while London's averages cluster around 562–615 mm — a difference of over 300 mm. The main counterargument relied on data that likely tracks London, Ontario (Canada), not London, England, and on cherry-picked individual wet years rather than long-term climate normals. Under the standard interpretation of "annual rainfall," Milan clearly receives more than London.