Tim Streater wrote:
Collected how?

By HMRC. They already have the information for all but 0.3% of income
tax payers of what local authority area they live in.

And allocated how? If I live in London and work in Brighton who gets the local income tax?

The London Borough that you live in. Local Government taxation is a
residency taxation.

All the details of local income tax has already been worked out. If
there was the political will to implement it, it could be implemented.

JGH