The new figures show the Government faces a desperate struggle to meet its literacy and numeracy targets in these areas, which are likely to face even closer scrutiny.
The analysis, which puts local authority test results in the context of poverty levels, shows that a string of new unitary authorities and a number of London councils are not doing as well as authorities with equally deprived intakes.
Around 10 local authorities, including Liverpool and Bradford, are further behind the national average than last year.
The figures will be particularly worrying for Newham, a flagship Labour borough which appears to be badly under-performing at key stage 2. It recently won plaudits from ministers and the Office for Standards in Education describing it as a model local education authority.
The Government has already decided to speed up inspecting authorities and to take over those which fail. Around a third of the 20 already inspected have been found to have serious weaknesses.
Education Secretary David Blunkett has promised that by 2002, 80 per cent of 11-year-olds will be performing at the expected level in English, and 75 per cent in maths.
Authorities which fall behind those with similar poverty levels - measured by the proportion of pupils eligible for free school meals - will come under the spotlight in ministers' drive to meet the English and maths targets.
The largest authority which appears to be doing badly at key stage 2 is Bradford, which asked for its inspection to be postponed because it has embarked on a major re-organisation. The others include two West Midlands authorities, Sandwell and Walsall.
A number of newly-created unitary authorities are struggling. The ones with results much poorer than might have been expected are the City of Nottingham, Thurrock, the City of Peterborough, Milton Keynes and Poole.
In London, primaries in the boroughs of Westminster and Hammersmith and Fulham are achieving better scores than Lambeth and Southwark.
Newham has the second lowest scores in the country in the latest published results for 11-year-olds. Although its rate of improvement over the past year is slightly better than the national average, The TES analysis suggests it is still performing far worse than might be expected on the basis of free school meals.
Tests show a serious decline in standards over the 12 months in some areas. Nationally, scores in maths fell by 2 percentage points, after a new test of mental arithmetic was included.
But Rotherham recorded a nine percentage point drop in its maths results with a smaller decline in English.
The test results mask serious problems in boys' performance in English. Barking and Dagenham in Essex is the third most improved for literacy, but it has widened the gender gap.
Girls' performance rose in 1998 by 12 percentage points, outperforming boys by 24 percentage points.
The London boroughs of Hackney and Tower Hamlets have improved their standards of literacy, but boys' scores have remained fairly static.
David Blunkett has pledged to resign if the targets are not met.
Analysis, 6; Leader, 18