I've heard both Jenny Harries and Dr Hilary say that children don't transmit the virus so the teachers are "ok" with them, but not other adults at school? Has this been confirmed? I've not heard anything!
Transmit the virus to who? There was reporting in the media that there was no evidence they could transmit the virus to adults, but this is not true fullfact.org/health/children-transmitting-coronavirus
There are various studies looking at transmission rates in children (bear in mind all of these have been done during lockdown, not during normal school attendance). Some suggest the transmission rate between under 10s is lower than in adults, but there's at least one which suggests it's around the same. AFIAK, there are no studies that suggest a 0 transmission rate between children. For children of Y10 age (so 14-15) the limited evidence I think suggests a transmission rate similar to adults.
In Denmark, since schools have reopened, the R rate has gone up by 0.3- this may not be due to child-to-child transmission, but I think it's still relevant.
More evidence is needed, and we don't really know, but saying children don't transmit the virus is rubbish and if government advisors have said this, then they are definitely lying.