But six have seen their departments decline, five losing their three-star rating.
The 18 successful authorities, which include Trafford, Lewisham and Warwickshire, mean that 55 of England's 150 authorities are offering excellent services, according to the Audit Commission.
Most LEAs retained the same scores as last year, with just 29 changing in the assessments, published yesterday. Kingston-Upon-Hull, with no stars, remains England's worst authority. A total of 88 were given two stars for education, while six earned one star.
The results form part of the Audit Commission's comprehensive performance assessment of all council services.
Education scores are based on research by the Office for Standards in Education, which looks at factors including results, improvement, special educational needs, strategic management and behaviour.
Authorities are rated on a four-point scale from no stars (poor) to three stars (excellent) and the results are combined with those from other services to produce an overall rating.
Miriam Rosen, director of education at Ofsted, said the results were a "wake-up call for those LEAs who have gone down by one star". But councils such as Redbridge, in east London, and Redcar and Cleveland, in Yorkshire, said they had been borderline last year and minor changes caused them to fall from three stars to two.
Walsall, which was judged to be failing and forced to call in help from a private company, Serco, has now reached the upper end of the two-star rating.
The authority says its performance will be further endorsed by a separate Ofsted report early next year which will show the largest ever improvement between inspections.
Annie Shepperd, chief executive, said a change of political leadership and management had eliminated what the Audit Commission described as a culture of bullying and intimidation by elected councillors of the authority's staff.
"All the energy that goes on in-fighting is wasted energy: we wanted it to go into schools and the children who go to them," she said.
Hackney, which is now run by a private Learning Trust, has also continued its rise from one star to two, but private management has not helped Bradford and Waltham Forest rise above their one-star ratings.
Schools minister David Miliband said: "There are still too many authorities that are achieving a zero or one-star rating."
But he said the ratings had encouraged LEAs to raise standards and promised more support for poorly performing areas.
This is the last time education results will be published separately. From next year, they will be part of a combined rating for children's services, in changes introduced by the Children Act.
The full performance assessment figures are available from www.audit-commission.gov.uk
CLIMBERS AND FALLERS
The 29 education authorities that have seen their rating from the Audit Commission change since last year. Ratings, from three stars (excellent) to no stars (poor):
From two to three stars Blackpool, Brighton Hove, Calderdale, Cambridgeshire, Cumbria, Derbyshire, Dorset, Lewisham, Newham, North Tyneside, Nottinghamshire, Oldham, Oxfordshire, Sefton, Shropshire, Trafford, Warwickshire, Worcestershire
From one to two stars Barnsley, Hackney, Manchester, Nottingham, Walsall
From three to two stars
East Riding of Yorkshire, Redbridge, Redcar and Cleveland, Somerset, Sutton From two to one star
Isles of Scilly
How the 150 authorities scored: Three stars 55
Two stars 88
One star 6
No stars 1