The homeowner should have received a letter from the building control officer informing them that building regulations had been applied for, and all drawings met current regulations.
This would also have had their unique reference number, once building control have acknowledged the plans and started inspections it is down to the contractor to satisfy the building control officer that all work has been carried out as per drawings, if all the work is up to standard the building officer should sign of regardless of his file being missing.
First thing to do is show him the building reg?s notice and main plans, if these have been drawn up by an architect he should have a copy, and if all work has been carried out to the drawings this should satisfy the building control officer and allow him to sign off the conversion.
If for some reason this cannot happen you could always take out an indemnity insurance policy which would allow any future buyer to claim of the policy should any problems from the council arise in the future?
There is no time span on completion of work once it has started, you can take as long as you like to complete the work.