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Services are commissioned by CCGs alongside NHS England and NHS Improvement on a local, regional and national basis.
NHS commissioning
What does "on a local, regional and national basis" mean? what does "basis" exactly mean? and why do we use the preposition "on" before "basis"?
Comments  
JigneshbharatiWhat does "on a local, regional and national basis" mean? what does "basis" exactly mean?

You are seeing that careful, vague, codified language that beetle-like socialist apparatchiks use because they are terrified that one word out of place will send them to the gulag. "Basis" is practically undefined here, which makes it safe. I actually don't know what it means here, or "alongside", for that matter.

Jigneshbharatiwhy do we use the preposition "on" before "basis"?

Only because it is idiomatic.

Jigneshbharatilocal, regional and national

Have you looked for these words in a dictionary?