Local authorities provide the budgets to run schools. Because this includes the money to pay the teachers' salaries, they are their
de facto employers. However, everything else is run by school governors. For example, along with the head teacher, they allocate the budgets, set the rules and (within the flexibility allowed by the National Curriculum) decide what will be taught.
This link might also be helpful:
http://www.direct.gov.uk/en/EducationAndLearni ng/Schools/SchoolLife/DG_10038366
Chris