First, a definition of "local authorities", this is from clause 8 of the Bill which inserts a new clause (2B) into the National Health Service Act 2006:
(5) In this section, “local authority” means—
(a) a county council in England;
(b) a district council in England, other than a council for a district in a county for which there is a county council;
(c) a London borough council;
(d) the Council of the Isles of Scilly;
(e) the Common Council of the City of London.”
In effect this is saying that public health is the responsibility of county councils. This link is to a spreadsheet of all local authorities in England (county, unitary and district authorities). The source is ONS and it was collated by the Guardian.
From this spreadsheet we can see that the populations of the 33 counties vary between 404k and 2.6m (median size 760k). The interesting thing is that there are 152 PCTs varying between 90k and 1.3m (median 282k).
This means that public health is currently being carried out by authorities much smaller (around a third) than the authorities who will get the responsibility under the Bill. This is not localism, this is centralising power.