Three inner-city councils have finally agreed to co-operate with the Office for Standards in Education in a new inquiry into primary maths after seeking assurances that the exercise will not be turned into “a political football”.

The councils, Newham, Greenwich and Knowsley, have been worried that the numeracy survey will echo the report on literacy in three inner London boroughs, published in April this year.

This became a cause celebre when the boroughs - Tower Hamlets, Southwark and Islington - accused OFSTED of rewriting the report at the 11th hour, ignoring positive achievements and failing to account for the effect of social disadvantage.

The literacy report also sparked off a panic about standards in teacher training, which led eventually to the recent announcement of a national curriculum for teacher training.

A joint statement by three boroughs chosen for the numeracy study says that they needed to be reassured that they were not being persuaded to create a stick to beat their own backs because “the invitation coincided with what had been seen as an act of bad faith by the chief inspector in castigating teachers, schools and local education authorities that had participated in a similar survey of reading”.

OFSTED inspectors will join local authority inspectors in 15 schools in each borough. The schools are now being selected at random, and inspections will begin after half term and finish in December. The final report will be published next April.

Newham, Knowsley and Greenwich were selected for the study because they were representative of inner-city areas with poor numeracy. The director of education at Newham, Ian Harrison, said: “An exercise like this is, on the face of it, very valuable if it identifies strengths and weaknesses in primary maths teaching. If there are weaknesses, we want to know about them. Our only reservation was the way the three London boroughs were treated. Also, you can’t help being a bit suspicious that the three are all Labour-controlled - OFSTED did not randomly select Westminster or Wandsworth, we noted - and that the final report will probably come out just before the general election.”

OFSTED, he said, had assured them that the whole thing would be a joint exercise, with LEA inspectors working alongside the OFSTED ones. Jim Rose, head of the primary team at OFSTED, has promised that examples of good practice will be included, and according to Mr Harrison has admitted that the elision of positive evidence had been a weakness of the literacy report. OFSTED has also promised that the final report will include contextual evidence - in Newham, for instance, English is a second language for over half the pupils.

But the chief inspector has vetoed a suggestion by Graham Lane, Newham’s education chair, that the final press conference in April should be presented jointly by OFSTED and the councils. Nor has OFSTED relinquished any editorial control of the final report.

Standards of numeracy will be measured by researchers from the National Foundation for Educational Research, using the national curriculum tests.

The new study will also measure children’s facility in mental arithmetic. Mr Harrison said he was not expecting the inspectors to pillory his borough for the absence of whole-class teaching in maths partly because it was already used along with other methods, and partly because “when you have classes where large numbers of pupils have a poor grasp of English, then the value of whole-class teaching is reduced.”