You really don't understand what Secular means do you. To reiterate - from the NSS's vision statement:
'We campaign for a secular state in which all citizens are free to practise their faith, change it, or have no faith at all.'
That's what we have at the moment. You also forget the many, many schools that were founded as a manifestation of the practical religion people had.
Short of letting this fade naturally or not since the state has decided to maintain some level of religious involvement any secularist success in the field of education would seem to involve an overnight overruling of the status quo in a display of macho trouserhugging secularism that would not reflect popular will or the actual support for a wee group like the secularist. I can't think of one major party that would wish to go down that route.
Conversely I don't see much evidence that education is particularly part of any outpouring of modern British secularism as I see no particular secularist effort to establish anything educational apart from Graylings university which seems to have sunk into irrelevance.
What I am afraid of is the sometimes wilful caricaturing of what faith practice is and my fears that secularists consider faith to be something that can go on unadvertised behind closed doors something that is undoubtedly Stalinist. I highly expect also that in an ideal NSS world people would be able to trumpet their new atheism anywhere,at anybody,anytime.