The gentle, folk-song nature of ‘Golden Notebooks’ conceals some pretty advanced harmony. There really is no need to dissect it because of its simplicity. We can easily memorize and play variations on the piece without a lot of “Preparational Analysis”.

Mulligan creates tension and release in the first section, not by setting up a key centre, but rather with melodic activity and rest and his trademark counterpoint (Link).

One way to think about the “tonal palette” of the main theme (bars 2 to 9) is to alter a basic C major scale in different bars. Bar 2 has a diatonic ‘b natural’; bar 3 lowers the b to b flat; bar 8 has a lowered 7th (b flat) and 2nd (d flat/c sharp).
Bars 2 and 3 could be called a I-bVII progression in C but it sounds more like a II-I in Bb. Ultimately, it doesn’t really matter as long as we recognize the shifting B-Bb.

Aside: Some people would call the Bb chord and th A chord “borrowed chords” or “modal interchange chords” arguing that the chords are borrowed from related modes. If you like to “think in scales” bar 2, 4 and 6 are C major; bars 3, 5 and 7 are C Mixolydian and bars 8 and 9 are D harmonic minor.