Blair set in motion the legislation for academies, which made it easier for Gove, but it was never his intention to have the free schools and academies we now have.
The original academies were a last ditch attempt to improve failing schools. These schools were dire. At the time, the constraints of the National Curriculum meant that headteachers couldn't implement the kind of curriculum which was appropriate for pupils.
For example, there was one school where only one pupil out of a whole year group achieved 5 A-Cs at GCSE. There was a high teenage pregnancy rate in the area, so the head wanted to increase the time available for PSHE. He wanted to spell out to the the pupils the reality of teenage pregnancy, raise aspirations, so girls didn't think it was the 'only way' and, for those who did find themselves pregnant, improve knowledge of childcare. The National Curriculum meant that these pupils had to study traditional subjects, which the head felt were irrelevant. Blair took the decision to free heads from the National Curriculum by turning the schools into academies and allowing schools to decide what was best for their own pupils.
Gove used the legislation to allow all schools to 'privatise' themselves. The first Gove academies were schools which had been judged as outstanding by Ofsted, which then set about marketing themselves to cherry pick the best pupils.
It has resulted in the destruction of local authorities, which has had a number of effects,including the inability for local authorities to plan school places. That's why so many people can't find places in their local school. Ironically, control of schools has moved away from parents and local decision making to central government.
The problem I have with the Blair government re eductaion was his obsession with micro-management and his use of league tables, which have reduced schools to attainment 'factories', with so many schools gaming the system.
It's unfair to blame Blair for today's schools. He certainly wasn't responsible for the reintroduction of grammar schools.