Teachers neglect history, technology, RE, geography and art, according to the Office for Standards in Education, because the slimmed-down national curriculum is encouraging them to emphasise the core subjects of English, maths and science.
OFSTED's report, published on Tuesday, also notes that weak written work is affecting the performance of pupils of all ages across the curriculum.
The inspectors' analysis of standards in individual subjects elaborates on the chief inspector's annual report, and includes advice for schools on how to sharpen up their lessons.
The findings are based on the inspection of 3,476 schools in 1994-95. Primary schools were lambasted again this year by chief inspector Chris Woodhead, who found half "inadequate".
Teaching quality is a "key issue for action" in about 40 per cent of primary schools, according to this report, and the first two years of key stage 2 (age seven to nine) are the least well taught. Overall, the quality of teaching was "good or very good" in about two-fifths of lessons, but unsatisfactory in another fifth.
Inspectors highlight the problem of lack of subject expertise in primary schools and the continuing problems of time-management posed by the national curriculum. Only a minority of schools are staffed by teachers who possess between them the subject expertise necessary for the basic curriculum. The problem is most acute at key stage 2. There are shortages of teachers with main-subject qualifications in mathematics, music, science, technology and RE.
OFSTED recommends that schools carry out an audit of staff's subject expertise, persuade teachers to take in-service training, and encourage them to share lessons.
In English, standards in speaking and listening are "consistently strong", and the teaching of reading is also praised, especially at KS1, but writing skills are still too weak, both in English and other subjects.
Design and technology suffers acutely from inadequate accommodation, large class sizes and a shortage of equipment. Most pupils at KS1 are using only paper or card, the inspectors say.
In science, teaching standards decline as the children grow older, the main problem being shortcomings in teachers' own scientific understanding. In maths, there is too much emphasis on repetitive number work and too great a reliance on published schemes. Too many pupils lack the ability to calculate, and there is little emphasis on the purposes of mathematics.
Use of information technology is weak, again mainly because of teachers' own lack of training and time.
In key stage 1 history, teachers need to give "more attention to distant places and times", but at KS2 there is "an undue emphasis on breadth rather than depth".
Primary teachers still have a tendency to expect too little of their pupils and should take more account of variation in ability, according to the report. They also rely too much on one teaching method. Pupils need to be taught how to work independently, not just left to get on with it.
Setting, as advocated by Labour's David Blunkett last week, is becoming common in key stages 3 and 4, but the inspectors warn that when using it, "too much can be taken for granted about the homogeneity of the group".
In both English and history, inspectors noted that pupils have difficulty producing extended prose and discursive writing: "There is insufficient use of writing as a tool for thinking and intellectual development".
Underachievement by white working-class boys is now becoming apparent in primary schools. On Wednesday, Chris Woodhead, writing in The Times, called it "one of the most disturbing problems we face within the whole education system".