Well, this is quite a well-known car in the club and you're sure to find any classic car trader will always add a significant extra premium onto whatever you'd otherwise expect to pay for an equivalent car from a private seller. And I suspect they've little choice!
Firstly, of course, because any dealer has to be able to run their business at sufficient profit to make an actual human living. (They're not a vehicle-preservation charity, after all!)
And also because said traders are commercial businesses which mainly sell-on to private persons who in law buy 'as consumer' - i.e. with the benefit of all those protections & entitlements which flow from their specific legal status.
Meaning any dealer has to cater for whatever it might come to cost them to meet statutory obligations towards a consumer who buys the car off them and then discovers a fault. Which, with any old car, is not only more than likely but could also - and very easily - incur all sorts of unexpected costs in whatever parts & labour are needed to repair/satisfy this strict statutory duty on the dealer. Although there've been a few (less reputable) car-dealers I've known of who went 'bust' specifically to avoid them....
As a business, a dealer's also got all the usual costs of running a business - including space or premises (whether purchased outright or rented) plus business rates; insurance; collection/delivery costs for their stock (incl. fuel & specialist vehicles or else hiring-in transport services) plus those other cashflow stresses which go with having stock laid-up unsold. Not to mention the considerable expense of advertising that stock, both in glossy magazines & online.
All of which considerations - and especially those re consumer-protection in law - are probably what prompt many people only to consider buying their next classic car off a dealer. As well as bump up dealers' prices. Considerations which instead drive me, speaking personally, to do the very opposite and make it my policy only ever to buy cars privately - where that classic principle of 'Buying Nice Cars Off Nice People' has never failed me once.