Two-thirds of around 2,000 adults in the first tranche have succeeded with flying colours, removing them from the stigmatised group, say ministers.
But, while welcoming the results of the controversial programme, others have urged caution in attributing too much to the results published this week.
The short courses and tests, recommended following the Claus Moser report, were likened to the "driving test" and sharply criticised as simplistic by many basic skills providers two years ago. But the Government went ahead with them as part of its pledge to cut the number of illiterate and innumerate adults by 750,000 in three years.
Four tests at levels 1 and 2 (equivalent to GCSE D-G) are administered by City amp; Guilds and Oxford Cambridge and RSA Examinations. The Department for Education and Skills says 1,251 of 1,915 who took the tests have passed and are no longer among the seven million people thought to lack basic skills.
"The success rate was around 65 per cent, which is a fantastic effort," said Estelle Morris, the Education Secretary. "The results show that, where adults are given the opportunity to learn literacy and numeracy skills, they can get on and improve their lives."
The literacy test pass rates were 64.4 per cent at level one and 63.8 per cent at level two. In numeracy they were 70.5 per cent at level one and 55 per cent at level two.
The figures should be treated with caution, according to Paul Convery, director of the Centre for Economic and Social Inclusion, especially as not all the people who took the tests had their basic skills levels assessed before training took place.
He says more thorough monitoring is needed of people's ability levels so the Government can assess whether the tuition is proving good value for money.
"One should not be simply looking at how many people are at a particular level," he said. "You need to know what distance they have travelled."
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