Was Milton thinking of King's Chapel?

This is from Il Penseroso by Milton. I once learned the companion piece, L'Allegro, mostly by heart.

But let my due feet never fail
To walk the studious cloister's pale,
And love the high-embowèd roof,
With antique pillars massy proof,
And storied windows richly dight
Casting a dim religious light.
There let the pealing organ blow
To the full-voiced quire below
In service high and anthems clear,
As may with sweetness, through mine ear,
Dissolve me into ecstasies,
And bring all Heaven before mine eyes.