Not sure why you are looking at Virgin trains as they do not operate this route, Southeastern is the operator -tickets.southeasternrailway.co.uk/se/en/JourneyPlanning. You can possibly book through Virgin, but they would just act as an agent.
I am planning a trip that will take me from Dublin, to Ironbridge Gorge/Black Country, York, Oxford, London plus a couple day trips out of the city, and then back to Dublin to fly home. That is rail and ferry service accross 10 train operating companies and their respective routes.
While trying to make myself familiar with the rail system, I have learned that National Rail is great for a journey planner, but that website does not handle tickets. In turn I have also learned that ALL train operating companies also have journey planners and sell tickets for ALL other train operating companies and their routes and services -- well except for the sail-rail ticket, which I need to get through Virgin Trains.
Now, while all TOCs sell tickets for all routes, they do not have a uniform ticket delivery policy. Not all companies offer e-tickets or mobile-tickets. Many only deliver tickets to UK addresses. And not all companies have a self service kiosks -- as in Arriva TW does not have a kiosk in Dublin (according to Arriva) that would allow me to pick up my ticket in Dublin, and Arriva only delivers to UK addresses.
Virgin trains however, offers the same journey planner, which also tells me who the operating companies are. Plus, Virgin Trains will ship all the tickets I buy to the US. I am already buying two tickets through Virgin Trains, why not get all of them?