Live or work in Rotherham, the neighbouring constituency to basic skills minister John Healey, and you have a wealth of choice: sugarcraft, aromatherapy, genealogy, Tai Chi, Indian cooking, and holiday French.

But in St Ives in Cornwall there is nothing on offer. Nor in Penzance, Hayle, Marazion or Falmouth.

In Enfield, Middlesex, you have gift-wrapping with style, handling exotic animals, personal presentation, tree identification, horse-grooming and seated massage. In the stockbroker belt of Sevenoaks only computing is on offer. In Islington there is self-development, but for asylum-seekers only.

The free courses, between one and two hours, are on offer throughout most of the country until July 21. They are aimed at showing people that learning can be fun and encouraging them to learn new skills.

An LSC spokesman admitted that the picture was “patchy”, but said they were reliant on providers putting on the courses ex gratia. Nearly 18,000 people had so far enrolled, and the target by the end of the period was 50,000. The biggest take-up had been in IT courses.

Government advertising for women-only bite-size courses could be unlawful under the Sex Discrimination Act, according to the Commission for Equal Opportunities.

Such courses advertised on the bite-size website include book-keeping in Oxford. No such courses are available for men in the city, where there are also CV-writing courses, again for women only.

A spokeswoman for the CEO said advertising women-only courses is only justified in areas of work where they are almost entirely excluded from employment.

“With women making up 74 per cent of the book-keeping and financial clerks occupation group, this wouldn’t apply,” she added.

The Learning and Skills Council is to investigate the claim, but stresses that people who have lacked access to post-16 education, such as single mothers, are just the sort of audience it wants to reach.

“If any of the advertising is found to be discriminatory, we will take it off,” said the LSC spokesman.