It seems to me that the definition of 'secularism' we are using is very fuzzy, and this is not helping the debate. So here are some things that seem to be under discussion:
The separation of church and state
The ending of involvement by religious organisations in state education.
The ideal of a religion-less society.
The ideal of society where religious belief is held to be a purely private matter, with no purchase on public life - whether this be civic, or moral, or constitutional.
Of these, I think I would say that the separation of church and state (in England, and in a modified sense in the UK more generally), may well have something going for it. The Church in Wales in already disestablished. But given the fact that House of Lords reform has just been effectively kicked into the long grass, it seems that it's unlikely to be at the top of the list of legislative priorities for any government any time soon.
The involvement of the church in state education is a historical legacy of the fact that the earliest schools for the poor were set up by churches - most notably the Church of England, but including other denominations and faiths. In none of the many reforms of the school system since the mid-nineteenth century has any government seen fit to unpick that historical legacy. And in the current climate, the idea that we will move to a single system entirely secular state education seems unlikely. And if I consider which likely outcome I would like least, having schools with church involvement in their running, or schools run for profit by private companies, I know which I would choose.
Another shibboleth of secularists is the requirement to have acts of worship in schools. It seems to me that opposition to this bespeaks a certain lack of confidence in their own values on the part of secularists and atheists. If these groups are so worried by the infection of religion by the occasional exposure to Christian or other worship, then they must be worries indeed about their ability to transmit their moral values to their children.
Finally, on this topic, is the teaching of creationism in state schools. In schools that are bound by the national curriculum, this cannot happen. And that presently includes all church schools.