I think Swale BC do this. Their scheme includes fixed award periods for those on UC, and also fixed earnings periods and tolerance levels. See para 15B, and 74A and 74B of their scheme.
Although check its the current scheme – their website version shows 2020/21.
https://services.swale.gov.uk/assets/Council-Tax-and-Business-Rates/Council-Tax-Reduction-Scheme/Swale-S13A-Final-Scheme-202021-v1.2.pdf
