My old lot has had, I believe, 3 instances of cowl departure on, umm, departure. 3 different types.
The 146 engine 3 cowls opened and snagged the throttle linkages/control lines and smashed the throttle back to the stop hard enough to bend it. Result was effectively an engine failure.
An E195 lost one in Jersey because the latches hadn't been fastened post maintenance. Continued to, I think, Birmingham with no adverse handling. They only found out after landing when someone mentioned they may have left something behind. Jersey airport authorities then found the bits, in the grass luckily
Q400 had one on rotation which damaged the leading edge deice boots, swift RTB but no adverse handling effects. Red faces were apparent, apparently.
It was only after the 195 incident that the cowl latches became part of the external check. They are right at the bottom of the engine and hard to see even if you're looking for them.
Maybe BA will amend their external checklist now, if it wasn't included already.