Is there a way of verifying a birdstrike incident which my airline is telling me affected a flight out of LGW early on Saturday morning
Doubt it, unless it was so serious it warranted a full blown Air Safety Report to the likes of the CAA...even then don't hold your breath.
Not knowing the airline involved I guess it is possible the birdstrike could have happened the previous evening when perhaps the aircraft returned to base or came for a night stop, and there then followed a long repair, or it might have been spotted by someone at the start of the day shift....and/or as DR has said the aircraft you eventually flew on may not have been the one involved in the birdstrike, all sorts of airframe "shuffling" might have been involved.
These things do happen and circumstances can lead to long delays - out of interest can you tell us why you are sceptical?