If someone comes to live with me will this affect my housing benefit and council tax benefit?

If that person is your spouse, civil partner or partner (same or opposite sex) then you will need to be re-assessed as a couple and that will involve taking account of your joint circumstances.
If the person is aged 18 or over, and lives with you on a non-commercial basis they will need to be treated as a 'non-dependant' for housing and council tax benefit purposes, and in most situations this will affect your entitlement. Normally a non-dependant deduction will be made from your entitlement based upon the circumstances of the person new to your household.
To prevent any overpayment of housing and council tax benefit it is always safer to report all changes in your household/family arrangements and the Council will then be able to advise if the change affects your entitlement.