I’ve done a few of these now, I’ve had the same request: make it less hot in summer and less cold in winter.
In this Polegate conservatory I install treated battens to the existing structure, insert a foam and foil based insulation tightly between the battens and foil tape up every join and gap, then the whole lot is covered over with an easy to clean upvc cladding material, which also has a 9mm air pocket to aid insulation, then all the edges are sealed with an exterior grade masitk to make the ceiling air tight and prevent insects/spiders from residing there.

Conservatory roof insulation finished Conservatory roof insulation part finished