OK, there are 2 things here - Planning Permission and Building Control approval. Planning Permission is about avoiding blots on the landscape, Building Control is about avoiding the blots on the landscape falling down because they weren't constructed properly. Both are controlled (but through different departments) at your Local Council.
It is probable (but not guaranteed) that the conversion did NOT require Planning Permission (PP). It is certain that the conversion needed Building Control (BC) approval.
The indemnity policy would have been in respect of the BC element, in the event that BC find out about it and demand that the structure be completed to the required stds.
Have a look at your policy - I think you will find that it is invalidated if you go and talk to BC - but then that is the very thing you want finished off anyway!
Since the garage door hasn't been bricked up, I'm not clear what you have - what change in habitable space HAS been created so far in that garage? To make the space properly habitable (as far as BC are concerned) the main aspects are the structural integrity (unlikely to be a problem), ingress of moisture from below (what's been done on the floor - DPM + screeding over?), ingress of moisture through the walls (does it have a second skin been built inside the outer skin?), insulation standards (can be sorted by attaching rigid foam to walls, battening then plasterboarding). What windows are in there?
You would have to apply for PP to erect another garage to replace the old integral one.