I did read something about King John's Treasure a few years ago, it even gave a fairly contempory account of the incident, unfortunatly the books in my library, which is a bit of a black hole at the moment. But, from memory:
KJ & his train were crossing a ford on the Nene, there are a number of times a year that the Nene, has high tides, (not quite bores as on the Severn, but heading for that height), one of these tides got the train...
KJ, continued north to (I think Newark), where he died a few weeks later...
The site of the ford is known, (more or less) & searches have been made, the last one in the 1960's (I think), then they drilled down to a place where large masses metal had been detected, the drilling seemed hopeful, but later digging found nothing. They claimed that the underlying ground had moved between drilling & digging!!!!
Finally, there may have been no treasure in the first place, it is suggested that KJ, was already broke & the journey he was on, may have been an attempt to raise new funds.
If I can find my original info, I will post it, unless, someone gets in first!!!!!