I stick with BA because of the benefits of GGL for a family - but of course it takes quite some flying to get to that level.

Once onboard we very rarely get any special treatment, but the ability to enter lounges as a family is a great help, as of course is the ability to book redemptions pretty much where we need, even during school holidays.

As for other UK-based FF schemes which "get" it - I was Gold on VS for a long time but I don't remember them doing anything officially for families..

You can, of course, have a household account to share your Avios and get European SH redemptions with pretty good availability without needing to reach GGL.