The entire south side of Eastcheap was demolished in 1882 to allow the Metropolitan Line to be excavated, and in 1883 the firm of Peek Bros, Tea and Coffee Importers, built a grand new office at No 20 with a circular corner tower. To liven the tower up, they got William Theed the Younger to carve an alto relievo depiction of their coffee being brought across the sands of Araby on the backs of three camels led by a Bedouin in his flowing robes. It's straight out of Desert Song.
Theed loved exotic subjects, having done the Africa section on the Albert Memorial and a line of horses for Buckingham Palace.
Why is it so deadly serious but chuckle-out-loud funny at the same time? I think it is the way the driver is striding so purposefully with his robes flowing out behind, such is his determination to reach Eastcheap before the Peek brothers (Fred and Jim) get fed up with waiting and go to the pub.