Jones is nominated for "Driving Miss Daisy," Law for "Anna Christie" and Spacey for "Richard III," alongside Benedict Cumberbatch for "Frankenstein," James Corden for "One Man, Two Guvnors" and David Tennant for "Much Ado About Nothing."
The prizes are decided by public vote.
The best actress nominees include Vanessa Redgrave for "Driving Miss Daisy" and Kristin Scott Thomas for "Betrayal."
In the musical categories, there are multiple nominations for the movie-inspired romance "Ghost" and Roald Dahl-based "Matilda."
Winners are set to be announced Feb. 19.
The Associated Press contributed to this report.