Contribution based esa and ending uc

Hi, I am on high rate pip and have been on contributions based esa. We were put on uc last year and because we have more than £16k in savings (old accident compensation), we are on transitional protection and obviously after 12 months that's just going to stop dead..... What I'd like to know is, I assume I will just continue on contributions based esa? I have never been told that claiming uc converted me to "new style esa", but even if I was I assume that will continue even without claiming uc? Many thanks.

By stopping dead, I mean as we have £16k+ savings we are no longer eligible for uc, so any payments under transitional protection will end.

The compensation was nearly 20 years ago. And was invested rather than being put in a protected fund at the time.