Yes, eligible BA passengers have access to the Airport run lounge in T1 - it's upstairs above security ( there's a stairs/lift just after you go through security )

Do not plan to arrive early to go there, it's really not very good .. if you've got a little while to kill it's an acceptable place to sit if you can get a chair ( they removed a load of them because COVID and haven't put them back unless they have very recently ) .. Ok selection of food , drinks no longer self service ( Again because COVID )