AFAIK, your priority for housing will remain the same - your wages, or those of your partner are irrelevant for social housing. Whether or not you are working or have a wage coming in has no bearing on whether you can pay your rent. Goodsoulette is incorrect that you should tell them ONLY if you get HB
However, if you have a wage coming in your HB will definitely be affected - yes, you will have to notify the council he has moved in.
You will also need to contact the IR if you are in receipt of any tax credits