Strictly speaking they do. However, if booked through a TA, consolidator or a channel that is not directly BA themselves, they may use another fare bucket for the Domestic sector (albeit one that is combinable with a CE fare bucket) - not exactly sure which fare buckets on UK Domestic flights are combinable with CE flights.

I have never seen BA offering UK Dom connections to CE in anything other than J/Y, but that doesn't mean it hasn't happened in the past if someone booked through the BA call centre for example and the agent used the lowest available fare bucket for the UK Dom sector.