There have been several threads asking questions about whether children can still move between houses whilst isolating, finally the government have clarified:
researchbriefings.files.parliament.uk/documents/CBP-8901/CBP-8901.pdf
It's a "no" if they're isolating as a close contact.
Weirdly though, it doesn't mention what's allowed if the child has tested positive or has symptoms! I presume it's also "no" but am surprised they haven't explicitly stated this.