And be warned that is a hard and fast deadline measured to the second. There is nobody worth appealing to as the gates at the entry to security will not let you through from 18:30 (BA 1438 departs at 19:05)
BA offers a same day change facility on most commercial tickets that you can do online if you want. Just do not check in for your original flight and you can make the change (subject to available seats) at your leisure on Friday on MMB.
Later on Friday there are two further flights to EDI
BA1454 at 19:55
BA 1464 at 21:00