OK, in case this is of help to others, I think I have fixed it.
I had to uninstall the wole thing. I backed up my characters first (copy the folder C:\Users\HP\Documents\BioWare\Dragon Age 2\Characters and paste to your desktop), then uninstalled using the Windows Add/remove programs function. Then, making sure I was logged into both Origin and the Bioware social site, I redownloaded and installed the game from Origin (which downloads and installs your addins as well). Still logged into both I opened to play for the first time and went directly to Downloadable Content in the menu before doing anything else. I got a prompt to log in, and I logged in using my Bioware social site details.
My DLCs were there, and where before they had said 'unauthorised', they now say 'version 1.0'.
The live chat help guy explicitly said I wouldn't have to uninstall and reinstall, but this seems to be the only way to do it.
Uninstalling DOES lose your characters. I'm hoping that pasting them back into the same location they came from (note, this is NOT the same location as the rest of your game files (see above), which are saved in Program Files automatically) will restore them, but if they're gone, they're gone. I have played teh game through once, but as I'd wanted to play it through with these DLCs I don't mind doing it all again.
BUT THIS TIME WITH A DOG.
