That schedule in full (as at 29.06.2016):
Monday - Friday
( 01:00:00 - 06:00:00 ) Thames Radio Nighttimes
( 06:00:00 - 10:00:00 ) Breakfast with Chris Blumer
( 10:00:00 - 11:00:00 ) Pat Sharp - The Top Ten At Ten, followed by:
( 11:00:00 - 13:00:00 ) Pat Sharp
( 13:00:00 - 16:00:00 ) Neil Francis
( 16:00:00 - 20:00:00 ) Drivetime with Neil Fox [Friday: Neil Fox Kick Starts The Weekend!]
( 20:00:00 - 22:00:00 ) Non-Stop Thames
( 22:00:00 - 01:00:00 ) London's Love Songs
Saturday
( 01:00:00 - 06:00:00 ) Thames Radio Night-times
( 06:00:00 - 08:00:00 ) Weekend Breakfast
( 08:00:00 - 12:00:00 ) Neil Fox - All Time Favourites
( 12:00:00 - 14:00:00 )Totally 80s - Martin Buchanan
( 14:00:00 - 18:00:00 )Neil Francis
( 18:00:00 - 21:00:00 ) Tony Blackburn's Soul Party
( 21:00:00 - 01:00:00 ) London's Love Songs
Sunday
( 01:00:00 - 06:00:00 ) Thames Radio Nighttimes
( 06:00:00 - 08:00:00 ) Weekend Breakfast
( 08:00:00 - 12:00:00 ) Pat Sharp's Chilled Sunday
( 12:00:00 - 14:00:00 ) Totally 90s - Martin Buchanan
( 14:00:00 - 22:00:00 ) Non-Stop Thames
( 22:00:00 - 01:00:00 ) London's Love Songs
If the breakfast host is already doing two separate daily shows in Wales, then my guess is that not one single show is live. I'd say that the studio is actually a server running somewhere in Wales. Happy to be proven wrong, though.