Their children, however, do speak English. Indians born from the late 1970s on are 99 per cent fluent. Young men from Pakistani and Bangladeshi backgrounds are only a little behind. Women from South Asia have made still more striking progress. Only 2 to 3 per cent of first-generation Bangladeshi women were fluent in English; now nearly 80 per cent of Bangladeshi women aged between 16 and 23 are.
That transformation is worth celebrating. The new report on ethnic minorities and the labour market from the Performance and Innovation Unit in the Cabinet Office, from which these figures come, says rather snootily, "as might be expected, the proportion who speak English well increases with the length of settlement in Britain".
But there was nothing automatic about it. This was a chancy and difficult social process wrought in the schools of West Yorkshire, Hillingdon and the Manchester conurbation by teachers, and by the governors and local education authorities who put resources their way.
Education, so often the villain of the piece, secured a remarkable triumph. Schools succeeded in doing what they are supposed to: teaching children life skills.
Arguably, they bore the brunt of adjustment for post-war non-white immigrants, especially in areas where Asians had to acquire language skills . There were some allocations: Section 11 money, for example. But there was no national plan for reception and "acculturation". Teachers had to make the decisions about whom to teach and how. Without actually admitting it, the report says that teachers made the right call: children did acquire the language; many gained the qualifications.
The report makes no policy recommendations; they are meant to come later. Some of its research was commissioned from Anthony Heath, professor of sociology at Oxford. His argument is that there are no big differences in educational attainment between the white majority and ethnic minorities, at least nowhere near enough to explain the differences in pay, jobs and status in the labour market.
If so, one of the reasons for underachievement at work has to be continuing discrimination by employers, and private-sector employers at that, since it has been in the public sector (health and education) that black Caribbeans and Indian women have made their advance into professional employment.
No one disputes that educational underachievement remains, nor should we fail to notice important differences between groups, especially people of Indian and Pakistani descent. The figures cited expose the failure of adult and continuing education in the lives of many Asians. Yet it would have been reassuring if some of the ministers to whom this report was circulated before publication, especially Estelle Morris, had drawn this conclusion. Schools (and further education colleges and universities) have added to the country's human capital by giving the sons and daughters of first-generation arrivals knowledge and skills.
Men born in the two decades after 1960 were much better prepared for the world of work than their fathers: 18 per cent of black Caribbean men of that "first" generation gained O-level or its equivalent; 50 per cent of their sons. Some 4 per cent of first-generation Pakistani men had degrees; 15 per cent of their sons have them.
"The story", the report notes, "is of significant progress. Ethnic minorities born in Britain have substantially caught up with British-born whites and in the case of post-compulsory education, Indian and Pakistani men and women have overtaken their white counterparts."
So schools and colleges have done their bit. Yet companies, employment agencies, the courts and employment tribunals seemingly have not played theirs. Educated to attain, ethnic minorities are prevented from realising their abilities. In Anthony Heath's words, "It's a depressing story of continuing disadvantage."