If you run a business and people steal from you then you should be entitled to take appropriate security measures.

With a group, any group, milling around an aisle it is not possible for the cameras to spot who has put stuff in their pocket. I have witnessed it, not in Sainsbury's but locally.

Tolerating minor crime only encourages the individual to move on to more serious crime.

I don't suppose the children will be banned when accompanied by an adult so the ban seems proportionate to me.