If you are connecting to a same day business class flight then you'll have lounge access, regardless of what booking class you are booked into. It sounds like you are flying the business class leg the following day though. If your EDI flight is showing as D class that you should also have access as it would be booked as 'Business UK' but you might want to confirm this with the agent when checking in at EDI.

Note that there is no business class on domestic services, it's all economy.