Stage by stage
Commencement, excavation, foundations, damp-proof course and over-site, drainage, structural work, insulation and completion. At each stage they check the specific items listed in the Approved Documents.
What they do not check
Workmanship, finishes, decoration, brand of materials beyond what is specified, contract terms, payment milestones, or whether the design is sensible. None of that is in their remit.
Why this matters
A signed Completion Certificate confirms the work is compliant. It does not confirm the work is well built. That distinction is where most homeowner disappointment comes from.