But if you google on the phrase, you find that it doesn't seem to be Emma's invention. For instance, on a website on Belgian law, we have "Belgian legislation has also created a hybrid entity, the social purpose company, which can be considered as an alternative to non-profit associations. Unlike these associations, a social purpose company may perform a commercial activity, but this activity should be carried out in a non-profit context." This is more or less what we would call a social enterprise; it doesn't describe A4e. Then there's an internet selling company called OneNest which sells artisan goods. It's founder says, "Exactly ten years ago, I created my first social purpose company, oneNest." And, "Global Partners & Associates is a social purpose company working to promote democratic politics, effective governance and human rights."
So the phrase can mean whatever you want it to mean. What A4e apparently wants it to mean is that they're not like all those other private companies, like Serco, Capita, G4S et al, which take whatever contracts they can get in order to make a profit. No, A4e sees itself as blending "commercial and social principles" and coming up with something new. They've got a long way to go to persuade many of the people they've had dealings with that this is the case.
And as a PS, I wonder why there are almost no comments under any of Lovell's blog posts.