'My builder issued a certificate — am I covered?'

Only if they are registered with the relevant competent-persons scheme for that work. Ask which scheme, get the membership number, and check the public register.

'Do I need a certificate for every trade?'

Not every trade — only the ones where competent-persons schemes exist (windows, gas, electrics, solid fuel, ventilation). For structural and building fabric work, Building Control sign-off is the equivalent.

'What if a trade certificate cannot be produced?'

Treat it as work that may not be compliant. Get an independent opinion before paying the final invoice.