In this case, since the site was 20 hilly miles from the nearest station, which would have been a not very fast train from Londonton, we hired a car. A Ford Focus fitted all our camping gear, two folders, three people, and a bunch of extra blankets.
It was a planned trip - Association of Lightweight Campers Early Birds meet. Best to book trains at least a week in advance, but we've come a cropper with early booking and not being able to book bikes on until much closer to the date.
Another issue is when they decide late on to replace a crucial section with a bus link.
Butterfly mentions that a Network Card is helpful, and we also have a Family & Friends railcard, which is useful when we have a bairn with us.
tbh, we do very few spontaneous camping trips, as so many of our weekends are booked up with meets...