Hi Ali B
I have moved your post. We ask members not to ask questions on someone else's post as it it can become confusing. You added yours to a post that was four months old.
Your question is outside the remit of this forum, but transitional protection is paid to ensure that people are not worse off UC than they were on ESA. So as far as I understand the system, a change of housing won't affect that. You can ring the UC helpline to check.
BIS
Nothing on this board constitutes legal advice - always consult a professional about specific problems