In spite of the provocative title of the book, Does Education Matter?, Alison Wolf is no fool. She admits that (1) yes, knowledge, and thus education, is important in itself. She admits that (2) yes, education has an effect on the salary an individual can gain. As a "positional good" it affects how the wealth in society is distributed. This is because employers use higher education also as a proxy of different abilities like intelligence or motivation, and only partly as an indicator of concrete skills. Furthermore, Wolf admits that (3) yes, education at the primary and secondary level has an important effect also on how wealthy, in absolute terms, a given society can be. The important concrete skills employers are looking for are, quite simply (but not at too trivial level), reading, writing and mathematics. She even admits that (4) yes, education at the tertiary level can create wealth, provided it creates high quality research and professionals. But here we are already close to a "no" answer (which you all knew was coming).
In Western Europe, about one third of a cohort get a university degree, and we are on our way to the level of two thirds already reached in the USA. There is preciously little evidence that this expansion creates economic growth; if anything, it is a result of such growth. Symptomatically we have not seen similar expansion in the resources provided for the universities. With funding per student, also the teacher/student ratio has decreased dramatically, implying decreasing quality of the education ("efficiency gains" in education are problematic). Moreover, the overemphasis on tertiary education has made it more difficult to provide high quality primary and secondary education. As Wolf points out, the chosen policy most likely hurts the economy!
According to Wolf, however, there is little one can do to decrease the popularity of the tertiary level education. Young people are optimistic about their abilities and they - and their parents - want to keep the option of high future salaries open as long as possible. (This is why it has been so difficult to upkeep and create more vocationally oriented options for secondary or tertiary education, even if it might be more efficient.) At the same time, the politicians are not going to restrict university attendance by increased fees or by demanding higher academic results from the enrolled students; such options would simply be too unpopular among the voters. What is good for individual may be bad for the society.
In the USA the problem has been solved by letting the universities to compete, and thus creating stratification in the sector. In the more or less nationalized European education this is problematic, but perhaps less so than the options mentioned earlier. Best universities could this way get funding that is necessary to provide the highest research needed both economically and culturally (just take a look at the US Nobel Prize winners).
So, referring to "education, education, education" as a sure way to national riches is erroneous, not because education is unimportant, but because of diminishing returns: it is possible to have too much of a good thing, when it comes with costs. In similar vein Wolf explains - with excruciating UK specific details - the waste of resources when politicians and even business organizations have tried to "improve" the post-compulsory, i.e., vocational, further and university education.
In addition, expansion of tertiary education is not very effective way to help the poorest people of the society. In fact, the opposite is true, as it is the middle class that swamps the universities, widening the economic gap. A much more effective tool seems to be wage subsidies promoted by, for example, economist Edmund Phelps. Unfortunately, middle class voters (and thus also politicians) prefer investments in education, since they can profit from it. And as far as the education is concerned, socially conscientious people should pay more attention to the primary level, where the long term future of kids can be affected more.
Finally, concentrating solely on the relationship between education and economic growth impoverishes our world view and culture. Education is important in itself, and economy is important even when it is helped by the growing service sector.