Lynn
If you are only receiving ESA(CB) and do not receive any other benefits that fall under UC such as Housing benefit then you will not be moved to UC.
If you are also receiving ESA(IR) or another "UC" benefit then there has been no update, the plan is still to start the process next year but it could literally be years before an individual claimant is contacted.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems