A copy (or rather type-up version) of Archie Mountbatten-Windsor's birth certificate was yesterday obtained by the British Press Association and spread to the media. The copy can among others be viewed here.
Archie Mountbatten-Windsor, the firstborn child of the Duke and Duchess of Sussex, was born on 6 May 2019. His name was made public 2 days later.
The birth certificate confirms that Archie was born at The Portland Hospital in Westminster, London, as The Daily Mail had already claimed to know. Other than that, the certicate doesn't tell more than we already knew. That the Duchess of Sussex has the rank (in the certificate listed as «Occupation») as Princess of the United Kingdom is known to anyone with the slightest knowledge of the British Royal Family. Thankfully Archie's mother is styled as Duchess of Sussex and not «Princess Henry».
Anyway, the historians and genealogists can now rest satisfied that the question of Archie's birth place has been confirmed.