I am so sorry to hear this. Someone somewhere is being a jobsworth.
It used to be the case that you could order remotely from any dealership, which many people did in order to take advantage of offers. About 6 years ago, Marshalls VW South Oxford (Didcot) were offering £500 off Tiguans and many of us on this forum ordered one from them if our local VW dealer wouldn’t match it (which they wouldn’t). Other dealerships complained when they realised that they were losing business and it became a condition that you could only order from a dealership if you went there personally.
However, other than this slightly petty Motability rule, there is no reason why you shouldn’t be able to have the car. This is an issue that Motability should be able to resolve. The dealer won’t be able to, as if the order has been cancelled they can’t input a new order for a car no longer on the scheme. After @Elliot son’s problems, it does perhaps point to an issue with the dealership though, who may well have cancelled the Motability order themselves and blamed Motability.
It could well be that the dealer has nabbed it for a retail customer, but where that argument slightly falls down is that only around 25% of private buyers choose the 35 model and almost none would order a base car with no options, so a Motability order of a 35 model, especially if it doesn’t have all the desirable options, wouldn’t be that easy to sell. However (at the risk of contradicting myself) if they were going to be stuck with it you’d think they’d be fighting your corner for you.
My advice would be to speak to Motability again and if they won’t budge say that you wish to make a formal complaint (against Motability, not the dealership). That might get you through to a manager who may have the authority to overturn a poor decision made by a minion. In the meantime, let the dealership know that you are doing this so that they don’t sell the car, or pass it on to another dealership. If you make a formal complaint, you may well find that Motability come back to you and say that the order was cancelled by the dealership and not Motability. If that’s the case, make a formal complaint about Marshall’s to Motability. They have a fining system for dealers who behave poorly. Good luck and I hope that this gets resolved for you. Let us know.