Hi AM
I am slightly confused by your post as you stated that you get both IR ESA and CB ESA. IR ESA is means tested whereas CB ESA is not. I can only think you received EDP (£21.20) under IR ESA as you were in the support group of ESA. There are no disability premiums with UC.
DWP are correct, you should not lose all your income, CB ESA support will stay in payment, PIP will also stay in payment. I believe you will only lose £21.20 pw, if you did not apply for UC.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems