A google search seems to indicate also that there is at least a mention about this in the book Rapid Fire: The development of automatic cannon, heavy machine guns and their ammunition for armies, navies and air forces, by Anthony Williams, and I have found some vague references about a Rheinmetall patent for this kind of projectiles. Also, apparently the Polish writter Igor Witkowski mentions in his book Truth about the Wunderwaffe that an area near Mieleck is still contaminated by uranium from World War II trials with uranium-core amunition.In the summer of 1943, wolframite imports from Portugal were cut off, which created a critical situation for the production of solid-core ammunition. I thereupon ordered the use of uranium cores for this type of ammunition. My release of our uranium stocks of about twelve hundred metric tons showed that we no longer had any thoughts of producing atomic bombs.
And what's more, in a Spanish forum it is said (in a post dated 31 January 2009) that some of those uranium-core anti-tank rounds, confirmed for Pak 38 and apparently also for Pak 40, had actually been found in the area of the ancient border between Poland and East Prussia (though I have been unable to find any other reference to this).
Now, most of what I have posted above smells of the usual mixture of Nazi supertechnology and conspiracy theories, with no hard data to back the claims. But if the quote from Speer's book is real, there may be some truth in it, so I am going to ask. Does anybody have any serious information about possible development, trials and use of uranium-core armor-piercing rounds by the Germans in World War II?