Yes indeed, west lakes, but not to the client or most of those who hear the story! If looks like BA and smells like BA? They might have a different call sign and IATA/ICAO codes but they wear the livery.
My guess is that Citiflyer is there for financial accounting reasons but, whether that is true or not, they will do what BA main board tells them. My (further) guess is that they will have the same operating instructions as main line.