I searched the topic a bit more and found this article:
http://www.ascasonline.org/windowMAGGI107.html
"This mark could be narrowed down to have been applied to the spoon between 29 May and 20 June 1837 - a mere 23 days. The last day of the year marking for the William lV era 1836-1837 was 28 May 1837. On 29 May 1837 the lettering for the next 12 months began, with B being used. However, William lV died on 20 June 1837 so a new monarch's head, namely the head of Queen Victoria, had to commence the next day."
It seems that the spoon can indeed be dated to that narrow time period and they must have had Victoria's duty mark made in advance if the change really happened instantly when she ascended to the throne. The spoon mentioned in the article is actually by William Eaton.