From my experience, I applied for the car at the dealership- All ID away taken, photocopied and a couple of signatures given.
This was late on a Tuesday, there wasn’t an instant approval. The dealership rang me back fist thing the next morning to say they had checked and it had been approved so they were going to go ahead and order the car- My wife then had an email from Motability with her online account details, where we can see the application has been approved.
Nothing else as of yet, but this was only last week. The fact they had you back to sign some documents, I don’t understand that. Should have all been done at the application stage?
it sounds to me like they have either delayed ordering the car until that signature, or there has been a delay. A delay is perfectly possible, but either way the dealership sound like they could be a little more open with you.
either than or they are genuinely expecting it just as you are. I’d give it another week, maybe two and at that point of still no car I’d ask in pretty strong terms for some kind of official update.