Excerpt from The Illustrated Encyclopedia of Royal Britain by Charles Phillips:
The following year King Richard’s 11 year-old son and only child, Edward, Prince of Wales died. Richard and his queen, Anne, were maddened with grief. The prospect of a Yorkist inheritance, so dear to Richard’s heart, began to look extremely vulnerable and when, in March 1485, Queen Anne died after a prolonged illness, rumours circulated that Richard had had her killed so that he could bolster his position by marrying his niece, Elizabeth of York.
Did Richard lll have something to do with the death of his wife? I doubt it. By all accounts we are led to believe that he and Anne had a great marriage. The loss of his son and then his wife would have been devastating to any loving husband and father. I do often wonder if he was interested in marrying his beautiful niece, Elizabeth of York. At the time it would have brought the former supporters of his nephew, Edward V back to his corner, so I can see the appeal of it to a ruling monarch.