The short answer is that no-one knows.
When local authorities want to bring forward a new school (in response to a need for school places) they can, and sometimes must, hold a ‘competition’, inviting and then evaluating competing proposals.
But the Secretary of State does not have to do it that way and he chooses not to.
As far as I am aware, there is no open process of inviting applications/proposals where it is considered a new school might be needed.
Would-be promoters of free schools seem to simply appply to the Department (certainly, they are invited to do so by the public materials on the web site and so on). And they are then evaluated on their ‘merits’ against some very broad-brush criteria.
There are no statutory requirements specific to that process. Nor specific requirements for how the Secretary of State should decide between competing proposals (e.g. where more than one promoter wants to bring forward a school in the same area).
But general ‘public law’ requirements apply (such as the obligation to take into account relevant considerations and ignore irrelvant ones).
And so too do general statutory requirements such as the Public Sector Equality Duty.
Certainly, I have heard of examples where competing (or at least overlapping) proposals seemed to be dealt with without proper process.
In Chandler v Secretary of State the Court of Appeal rejected an argument that EU procurement law (which would at least require an open process) applied to the then process of a University applying to be sponsor of an academy. It did so because the funding agreement that would result could be seen to be not a ‘commercial’ contract and because the University in question was not coming forward for financial reasons. With the new generation of free schools those things are less clear, particularly given that, as I understand it, the current reluctance to provide copies of free school funding agreements is in part at least explained on the basis that they are ‘commercially confidential’.