I would say that you ought to have some form of documentation confirming your order that includes details of the car, any options, the agreed price, the amount of any deposit paid etc. The order documentation usually sets out the contractual terms and conditions of the sale should include such things as the rights and responsibilities of the buyer and seller, your right to withdraw under the 14 day cooling off period required under UK consumer law, what happens to any deposit you might have paid if you needed to cancel (e.g. if your circumstances changed at short notice), etc, etc.
I would phone the dealer again and specifically ask for a copy of the order documentation. It could be that vehicle order documentation is all digital now so you may not get hard copies. If so, then it should be straightforward for the salesperson you dealt with to email copies to you.