what is my local education authority

LEAs generally have responsibilities for the funding and distribution of the funding for schools in their areas, they are responsible for admissions and the number of places at each school, they employ the staff that work in voluntary controlled schools and generally are responsible for the children in their care.
In England and Wales are councils which have responsibility for the education system within their jurisdiction.

We hope you find everything you need to meet your child’s special educational needs. Your views are important to us, let us know what you think by visiting the ‘sharing my views’ section.
Information and advice for parents and carers of children with SEND

Your child’s school or college will update you on their plans this autumn term. See staying well: children and families for more information and support available from local organisations.
Find training courses in Essex, information about funding for courses, learning for adults with disabilities and older people

One hundred and fifty English local authorities and all authorities in Wales have the strategic lead for education of children and young people. They have a legal duty to ensure that every child fulfils his or her educational potential.
Third of local areas face secondary school places running out within five years

Including support information for school governors and apply to be a school governor
Including find a school, apply for a school place, check terms dates

References:

http://www.foi.directory/local-education-authorities/
http://www.birmingham.gov.uk/localoffer
http://www.essex.gov.uk/topic/schools-and-learning
http://www.local.gov.uk/topics/children-and-young-people/education-and-schools
http://www.barnet.gov.uk/schools-and-education
http://www.isc.co.uk/schools/scotland/perth-and-kinross/