To those migrating to UC be warned about council tax support

For the working age it isnt, it varies from one local authority to another. The changes can be quite extreme, likewise they have independence on how they dish out the household support fund as well. Councils with higher poverty levels are probably more likely to have less generous CTR schemes.

Sorry to hear that, do they have a discretionary support scheme?

I don't work for, or with, CT, so I can't answer that question. I only know what information has been provided in this area. As someone who's only ever claimed PIP and never UC or ESA, I don't want to speculate on things outside of my experience.

The local change doesn't apply to me because my household pays full CT already. But I have met people in this area who are directly affected by the change, and seen their bills.