Most of the original antiquarians were little more than middle class treasure hunters. With a few notable exception their interest in the sites they dug revolved around finding grave goods. They chucked a lot of real treasure on the spoil heap (bones, ashes, pottery) in a frenzy to find something shiny that they could put on display somewhere. They wouldn't have seen it that way themselves of course. They saw it as an effective pursuit of knowledge.
To my mind Modern Antiquarianism shares very little with it's namesake. The ethos behind it (even for a train spotter like Fourwinds) is very different. Visiting a site is the focus, and nothing (but litter) is taken away. Only the fanaticism of the participants and the amateur nature of the pastime are qualities shared with the original tump diggers.
I agree with Pebblesfromheaven when she says the metaldetectorists are the closest we get to it now. Like the original antiquarians they think they destroy as much as they find. They don't see it that way themselves of course. They see it as an effective pursuit of knowledge.
Another thing to think about is the picture outside the UK, where forms of treasure hunting similar to antiquarianism are no doubt still be taking place.
K x