TUPE means you keep the old conditions and don't have to accept the new ones. Since the undertaking continues there is no redundancy.
If there were redundancy it would be from whichever company decides it no longer has a role that needs your services.
Except in practice the new conditions often become "necessary" for a business reason after a short period of time has passed, so TUPE only really works with ethical employers and there aren't many of them outside public sector..
Are you in a union? You should be.