Local councils do collect a "council tax", but it's basically a fig leaf to disguise a poll tax by just enough that people don't outright riot: https://en.wikipedia.org/wiki/Poll_tax_riots
And in practice, council tax is only about 55% of local council's funding, the rest coming from central government. And the councils do sometimes go (effectively, but not literally) bankrupt: https://www.bbc.com/news/uk-politics-66878229
Local councils do collect a "council tax", but it's basically a fig leaf to disguise a poll tax by just enough that people don't outright riot: https://en.wikipedia.org/wiki/Poll_tax_riots
And in practice, council tax is only about 55% of local council's funding, the rest coming from central government. And the councils do sometimes go (effectively, but not literally) bankrupt: https://www.bbc.com/news/uk-politics-66878229