Make sure he asks to open a BASIC account - not a full account. With a basic account some banks still do credit checks but others don't. Certainly try Co-op - they are generally very good. They even do basic accounts for bankrupts, & the only other bank doing that is Barclays.
He won't get a Post Office account - they are only for certain state benefits.
If he lives with you he probably doesn't have any utility or council tax bills to use as identity, but if he has a bad credit record he presumably has statements from credit or store card outfits, or something similar.