As far as the LAA Permit renewal is concerned, the annual inspection can be carried out by the owner(s), or by a someone employed by them the do the work. The LAA have a schedule for this inspection. Your LAA Inspector then attends and looks at whatever he/she (are there any shes?) wants to look at, and may require further work to be carried out at their discretion. When they consider the Permit may be renewed, they issue a form which you return to the LAA, along with the renewal fee which for average SEP craft is currently £180.
If the old Permit has lapsed, your Inspector issues a Permit to Test, and you then complete the flight testing required in the LAA document (see LAA website, the link is too long to post here).
This is mostly from memory, someone will say if I've got it wrong.
Not sure if this is the same as the microlight Permit renewal. Also can't comment on C of A situation.