Given your comment, I suspect there's not much correcting you, but for the sake of others who are interested in how treasure works in the UK:
If you find something that might be treasure, you must report it to a coroner, who will first determine whether it really is treasure. Typically treasure is something valuable or historically significant.
If it is treasure, an independent body will then value the treasure, and also make decisions about who the treasure belongs to - typically it will be split between the finder and the landowner. At this point, the treasure will be offered to a museum for the price set by this independent body. If the museum doesn't want it or cannot afford it, then the finder/landowner get to keep the treasure, otherwise the museum buys the object and pays the finder and landowner.
So ultimately, assuming you find something, you'll always get to either keep the item, or have someone buy it off you.
That said, there are stipulations around not being able to just go around and dig up anyone's ground, and you always need to get permission from the landowner before going treasure hunting. In this case, magnet fishing is apparently not allowed on rivers, hence why they figured out an arrangement to donate the sword rather than be paid for it.
EDIT: And if you want to watch a light-hearted comedy series about metal detecting, you can't go wrong with Detectorists!