The sword from the Thames (now in the British Museum) mentioned above may have been found in England, but I think it is unlikely to be of Anglo-Saxon manufacture. This sword falls under Petersen's type S. Examples have been found across Europe, from Iceland to Russia, but are most common in
Denmark (as a percentage of finds per country).
[Androshchuk, "Vikings and farmers", 2009]
At a minimum, this type is known to have been produced in Gotland, as shown by the discovery of a hoard of incomplete hilts and local-style jewelry.
[Gustafsson, "Viking period metalworking hoard...", 2011]
The surface of the hilt is covered with decorative designs of distinctly Nordic type, perhaps classifiable as being of the late 10th-century Jellinge or Mammen styles. Other type S swords with similar decorations have been found in Norway (C237, shown in
Swords of the Viking Age) and near the Danish emporium of Haithabu/Hedeby.
https://en.wikipedia.org/wiki/Viking_art#Jellinge_Style
The latter example shares the wire-wrapped grip as the Thames sword. This feature seems to be most common on swords of type S, with other examples coming from Iceland, Russia, Ukraine, Slovakia...
Canute himself is depicted bearing a type S sword in an Anglo-Saxon manuscript illustration. Ultimately it may be the Thames sword that has a better claim to a direct link with Canute, but as a Danish import brought to England by one of his high-ranking followers, instead of an acquired local product.