Coal traffic after the Royal Navy changed to oil

Did the Royal Navy still need Jellicoe-style coal traffic during the Second World War?

Not on the First World War scale: the fleet was overwhelmingly oil-fired, although some coal-burning ships remained and coal still moved extensively by rail and sea.

By 1939 the Royal Navy had largely moved from coal to oil, so the special naval coal system associated with the First World War was no longer required in the same form. Coal nevertheless remained a major industrial and power-station cargo. That distinction helps explain why coastal colliers and inland waterways stayed strategically important even after the battle fleet changed fuel.