As you point out, the advertised price is indeed an "invitation to treat" with no legal obligation.
However (as pointed out above by MJ ) the sales contract was entered into by the OP when he offered to pay that offered price. At that stage there was still no legal requirement for the dealership to accept.
Once the dealership accepted the OP's offer (and deposit) both parties had entered into a "Sales contract" which absolutely is legally binding. The fact that the OP has verifiable confirmation in writing from the dealership of all of this, should put him in a very strong position to insist that they honoured their half of the contract as legally required.
However (as also pointed out by MJ ) the t&c's may be sited as their "get out". Nonetheless Terms & Conditions should be intended to clarify the terms of any contract, but are specifically not permitted to circumvent the Sales of Goods act.
Imho it depends on how much you value that £9k disparity. If he were to pursue it doggedly enough, I personally would be very surprised if he was unsuccessful. However I do not expect they would want to to make it easy for him, so doing so may not be a very pleasant experience.?
Seasons greetings..