When Teresa May announced her decision to overturn Tony Blair's 1998 ban on new grammar schools, she inadvertently created unity between the two sides of a civil-war riven Labour Party.

Corbynistas and Blarites cheered to the rafters when shadow education secretary Angela Rayner declared she would ‘fight, with every breath in my body' against new grammar schools as she kicked off Labour's ‘Education not Segregation' campaign at its party's conference.

The issue of selective education certainly brings out visceral tensions that are likely to spill out into councils.

That small cohort of counties such as Lincolnshire, Kent and Buckinghamshire, which already have grammar schools, are keen to expand the provision. Now other local authorities are keen to sign up for the revolution.

According to media reports, Kent, Essex and Northamptonshire CCs as well as the Windsor & Maidenhead RLBCs and the Sutton and Croydon LBCs have all been hot off the mark to develop plans for new or extended grammar schools.

In contrast, Oxfordshire CC boasts that it is first local authority to publicly reject any attempt to reintroduce selective schools in the area.

And the issue can pit councils against parents. According to local press, parents from Nottinghamshire (which has no selective education system) are sending their children across the border to neighbouring Lincolnshire to benefit from grammar schools.

John Peck, Nottinghamshire CC's chair of the children and young people's committee, is vehemently opposing Mrs May's proposals as turning ‘the clock back to the 1960s when children were sorted into sheep and goats at the age of 11'.

In selective Lincolnshire, Labour group councillor Phil Dilks said: ‘Dividing and segregating children from their peers only serves to reinforce the deep divisions in our society, rather than challenge them.'

Everyone on all sides of this debate agree on one key principle: schooling should be about social mobility.

Schools minister Nick Gibb noted earlier this year that ‘a welcome consensus has begun to emerge that schools can – and must – be engines of social mobility'.

So Mrs May claims selective schools will boost social mobility as part of a vision ‘that works for everyone, not just the privileged few', while her opponents' main argument against grammar schools is that they won't deliver social mobility for the underprivileged.

But there are two major problems with this approach. Social mobility is judged via non-educational measures such as jobs and salaries. But the alleged causal relationship between employment and schooling skews the discussion.

The working class grammar school kids of the 1950s got good jobs because the economy was expanding. The comprehensive kids of the 1980s and today fare less well because of successive recessions.

So for those who want more people from disadvantaged backgrounds to be able to socially climb, the key is to create more jobs and stimulate a sluggish economy into productivity rather than tinkering with schools.

Once social mobility becomes the moral purpose of education, rather than a possible by-product, schools focus on ensuring pupils acquire the means of improving their earnings potential rather than their minds, of expanding students' employability (and class) prospects rather than their intellectual horizons.

Too often the secondary moderns of the past doled out a paltry fare of vocational, work-related subjects deemed relevant for non-academic pupils' future lives.

Is it progress when the pro and anti-grammar schools adopt the same philistine relevance and employability agenda, concluding, ‘who cares what you were taught if you end up in a middle class job' ?

Councils should avoid arguing for secondary moderns for all.

Claire Fox is director of the Institute of Ideas and convenes the Battle of Ideas festival, held at the Barbican, London October 22-23 www.battleofideas.org.uk