Stephen Twigg and Teach First

Stephen Twigg is quoted here in the Guardian as saying that:

‘While in government, Labour made huge efforts to raise the status and quality of teaching; introducing programmes like Teach First to attract bright graduates, linking performance to pay and giving heads greater freedom to remove under-performing teachers.’ (my emphasis)

Is this the case about Teach First? I did Teach First and my understanding is that it is an independent charity that is supported by the three main political parties, and that this has been the case from its beginning. Of course it is true that Labour were in power when it was founded, and that they supported it and helped it get established. But the word ‘introducing’ makes it sound like Labour had a far more active role than that – indeed it makes it sound like Teach First is a government quango created by Labour.

I may be wrong though. Can anyone else shed any light on this?