Do you have access to fast track and biz check in?
Perhaps arrive for when BA check in opens (4am?) and if using fast track you should be fine. We arrived at check in less than 2 hours before the other Saturday for the flight 30 mins before yours and we were fine. Standard security was queueing to the entrance barrier but we were through fast track within 10 mins. The economy and oversize check in queues weren’t pretty however.
You have scope for the MAN to arrive just over an hour late and hopefully at that time, the LHR chaos won’t have snowballed too much. If it has, your IAH may be delayed too.
Fingers crossed for you. If it does go wrong, think of the €600 pp BA should cough up!