While there are specific rules regarding the compilation of phone directories for use by the general public, the Information Commissioner's Office takes the view that they don't apply to 'restricted use' situations. (e.g. if you were to join your local bowls club, that club could include your contact details in their directory of members, sent out to everyone in the club, so that others could get in touch with you to arrange games):
https://ico.org.uk/media/for-organisations/guide-to-pecr-2-4.pdf
So you might not have any case here. Further, the DPA (together with associated legislation and regulations) doesn't automatically bar any organisation from passing on the data that it holds about individuals. It only requires that such actions must fall within the organisations registration under the Act. It would seem reasonable to me that the DWP should be able to pass clients' details on to relevant partner bodies in order for them to be able to fulfil their functions properly.
So, once again, I doubt that a complaint will get you anywhere. However if you still want to try, this is where you need to start:
https://ico.org.uk/make-a-complaint/your-personal-information-concerns/
I agree with you though about the pointlessness of many of the schemes that are meant to help people get back into work. I've been on the receiving end of some of them myself!