Hi JK2019
Some rules did change at the beginning of January this year for the worse.
if you move within the same local authority then you can still stay on legacy benefits, if you move to a new local authority area and have to claim help with housing costs then you will have to apply for UC, if this applies to you then seek advice from your local Welfare Rights Organisation before you move as you do not want to be caught up in the assessment phase.
Some areas across the uk are moving benefit claimants over to UC.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems