Winner of 3 TONYS, Rex Harrison, played two kings--one on film and the other on stage. Both it seems opposite leading female characters with the first name of Anne for an extra twist to this puzzler.
Henry VIII, ANNE OF THE THOUSAND DAYS, 1949 TONY, Dramatic Actor King Mongkut of Siam, ANNA AND THE KING OF SIAM, 1946, Rex's film debut.
His other TONYS were for: Professor Henry Higgins, MY FAIR LADY, 1957 Musical Actor Special TONY, 1969
Someone mentioned Richard Burton. Sir Richard did play Arthur in CAMELOT, and garnered a TONY in 1961. For an interesting twist to the Harrison-Burton connection he played Henry VIII on film in ANNE OF THE THOUSAND DAYS. Sir Richard was also cited for a special TONY in 1976. But Rex had 2 TONYS by the time Richard earned his first so by virtue of being the more TONY-Awarded of the two, and this category being THE TONYS, Rex is the correct answer.