The Air Ministry merged with the Admiralty and the War Office to become the MoD in 1964.
For some years I worked in a building (since demolished) opposite the London Weather Centre. Because our building was taller, their measurements, including whether it was a White Christmas, were made on our roof.
The definition of a White Christmas is broader now, and can mean snow falling anywhere in London. (Lying snow from a fall the previous day doesn't count).