Great photos, Nellie and Octavius.

The men shown in Nellie's first pic actually walk beside the horses, not the carriage. That position is filled by footmen whose livery is slightly more ornate. Alongside them are Yeoman of the Guard carrying their long partisans.

Below we can see the footmen and guards at the Golden Jubilee celebrations.



So that makes 4 postilions, 9 walking grooms (1 walks behind the coach), 6 footmen, and 4 Yeoman of the Guard. That makes quite a crew!