Most people I know are already perfectly aware of this, and are happy to send their kids back in September. So would I, if I was in the UK
Most people I know - including the parents of my pupils i have spoken to - are aware of the ending of bubbles, but have no or limited awareness of the fact that no close contacts in school will be identified (as Test and Trace have said they will not attempt to identify close school contacts, only those arising from contact outside school such as sleepovers) and that none will isolate.
The release of the flawed study about regular testing instead of isolation has muddied the water further, as many parents, and others including the BBC, have erroneously concluded that this - rather than zero action at all - is what will replace isolation in September in schools.
The current pre-August 16th policy of testing for identified categories of critical workers has, again, given the mistaken impression that testing will replace isolation post August 16th.
If I outlined the current policy to parents: 'In September, there is absolutely no limit to contact and mixing in schools, including e.g. whole school assemblies, but a family where all other members are actively suffering from Covid can send their child into school to sit next to your child for 6 hours a day', I am not certain that many parents would believe me, let alone be happy to do so.