The successful authorities, which include Birmingham and Liverpool, join 28 others which already have the maximum rating of three stars for education.
The results were published yesterday, as part of the comprehensive performance assessment, an annual analysis of services in all 150 local education authorities in England.
Most LEAs retained the same scores for education as last year, with only 27 authorities changing categories.
A total of 42 gained the maximum of three stars, 97 two stars, nine one star and only one authority - Kingston-upon-Hull - received no stars at all. Walsall's services have not received individual ratings.
The education scores are based on research by the Office for Standards in Education. Inspectors combined judgments on school improvement, strategic management, social inclusion and provision for pupils with special educational needs to reach a score from zero stars (weak) to three stars (excellent). These ratings were then combined with those for other services, such as social care and libraries, to produce an overall rating.
Four of the 20 authorities which saw improvements in education had received private intervention: the London boroughs of Islington, Southwark and Hackney, as well as Swindon.
The Audit Commission noted that, although Hackney's overall ranking for all services remained weak, it was "showing signs of improvement".
However, the most dramatic improvement in education scores was in Liverpool, an authority which was considered the third worst authority in England four years ago and narrowly avoided privatisation. Its rating rose from one star to three this year.
Colin Hilton, Liverpool's education director, said the change in 2003 was down to measures introduced several years ago which had only recently started to have an effect. These include a revamp of the city's admissions system and a drive to turn around schools which had been criticised by inspectors.
For seven authorities, the education results were particularly disappointing because they were worse than for 2002.
These included Salford, where drops in education and children's services scores led the whole authority to be classified as "weak".
Education officers in Salford said the rating decline was due to a change in Ofsted's assessment criteria.
The same claim was made by Phil Coppard, chief executive of Barnsley council, which also saw its education score fall from two stars to one.
"It is very irritating that we have to suffer this ignominy," he said.
"We don't dispute the underlying data, but we thought the formula would be the same as last year which would have placed us in the two-star group."
Mr Coppard said Barnsley hoped to improve its results through a shake-up announced this week, which will involve closing all 14 of its secondary schools and replacing them with eight new "learning centres".
Individual LEA scorecards are available at www.ofsted.gov.uk
LEA CLIMBERS AND FALLERS
Authorities are listed alongside their current education rating, which range from no stars (poor) to three stars (excellent):
Three stars: Birmingham; Blackburn with Darwen; Bury; Durham; East Riding of Yorkshire; Enfield; Havering; Liverpool; Redbridge; Redcar amp; Cleveland; Stockton-on-Tees; Wandsworth; Warrington; Windsor amp; Maidenhead Two stars: Bristol; Greenwich; Islington; Southwark; Swindon; Wolverhampton One star: Hackney Fallers Two stars: Herefordshire; Isles of Scilly; Milton Keynes; Plymouth; St Helens One star: Barnsley; Salford All remaining authorities retain the same ratings as in 2002.
How the 150 authorities scored: Three stars - 42; Two stars - 97; One star - 9; No stars - 1 (Unrated - 1)