Although not officially confirmed, it seems that the first flight with the new Club World Suite in BA's new A350 will be the 6th of August 2019.The new Airbus A350 planes that will be coming into service shortly, will have test runs on flights between London and Madrid for pilots and flight attendants.
Flyertalk user BotB has posted a calendar of the expected flights to be operated by the new A350 aircraft during August and September.
As said this is not offical yet, so there's no guarantee that this flights are realy flown by the new A350…
Here are the times for the flight numbers:
BA456 London to Madrid 6:20AM – 9:40AM
BA457 Madrid to London 10:55AM – 12:15PM
BA464 London to Madrid 4:45PM – 8:05PM
BA465 Madrid to London 9:20PM – 10:25PM