Insurance company refusing to switch insurance back to car after repair.

My daughters car developed a head gasket issue in May so switch the insurance to a second car we had while we tried to sort it.

In between the jigs and reels it only got sorted this month.

Passed NCT and running like clockwork, she tried to switch the insurance back to the car.

Cue runaround from the Insurance company. She never took the car off the road, but paid the back tax and fully taxed it prior to the NCT, so they're saying they needed a letter from the garage explaining the gap.

Letter provided. Proof of tax provided. NCT cert provided.

They're saying the won't switch it back, some nonsense of the letter (which has garage name, location, contact number, date, signed and stamped) is not on headed paper.

Sent them both a scanned copy and picture proof of the original.

They won't elaborate why, what possible reason could they have?

It took long enough to get a garage to look at it, and cost enough to get it fixed, and now the car is safe and roadworthy and they're being as awkward as possible.