How Britain watched and supplied the Great White Fleet

Did the Royal Navy have any particular concern about the Great White Fleet during its voyage?

Not especially; Britain monitored the voyage, and British colliers helped supply the American fleet with coal.

The Great White Fleet caused no particular British alarm, although Royal Navy ships kept watch along its route. The answer also exposes the logistical limits beneath the fleet's diplomatic display. American colliers were insufficient for the voyage, so British coal carriers helped keep the battleships moving. Global naval presence depended on commercial shipping and access to fuel as much as on the warships themselves.