Chart on the bottom here [0] seems to confirm parents assertion - cases for under 18s spiked after school reopening, but are now decreasing. Though atm schools are closed for two weeks (Easter holidays)
The data I shared is calculated from random population surveillance testing, and is the gold standard on measure of true spread.
The data you linked to is reported cases. Children often have very mild or asymptomatic cases so they are not tested nearly as much and thus many more cases are undetected in children compared to other age groups.
[0] https://www.theguardian.com/world/2021/apr/08/covid-uk-coron...