The following is a list of the IRMA's number-one singles of 1991.
| Issue Date | Song | Artist |
|---|---|---|
| 3 January | "The Christmas No 1" | Zig and Zag |
| 10 January | ||
| 17 January | "Sadeness (Part I)" | Enigma |
| 24 January | "Do The Bartman" | The Simpsons |
| 31 January | ||
| 7 February | ||
| 14 February | ||
| 21 February | ||
| 28 February | ||
| 7 March | ||
| 14 March | ||
| 21 March | ||
| 28 March | "Rhythm of My Heart" | Rod Stewart |
| 4 April | "Deep, Deep Trouble" | The Simpsons |
| 11 April | ||
| 18 April | ||
| 25 April | ||
| 2 May | "The Shoop Shoop Song (It's In His Kiss)" | Cher |
| 9 May | ||
| 16 May | ||
| 23 May | ||
| 30 May | ||
| 6 June | ||
| 13 June | "Light My Fire" | The Doors |
| 20 June | ||
| 27 June | "Any Dream Will Do" | Jason Donovan |
| 4 July | "(Everything I Do) I Do It for You" | Bryan Adams |
| 11 July | ||
| 18 July | ||
| 25 July | ||
| 1 August | ||
| 8 August | ||
| 15 August | ||
| 22 August | ||
| 29 August | ||
| 5 September | ||
| 12 September | "Hay Wrap" | The Saw Doctors |
| 19 September | "Don't Cry" | Guns N' Roses |
| 26 September | ||
| 3 October | "I'm Too Sexy" | Right Said Fred |
| 10 October | "(Everything I Do) I Do It for You" | Bryan Adams |
| 17 October | "Always Look On The Bright Side Of Life" | Monty Python |
| 24 October | "The Fly" | U2 |
| 31 October | ||
| 7 November | ||
| 14 November | "Zigzagging" | Zig and Zag |
| 21 November | ||
| 28 November | "Black or White" | Michael Jackson |
| 5 December | "Zigzagging" | Zig and Zag |
| 12 December | "Mysterious Ways" | U2 |
| 19 December | "Bohemian Rhapsody"/"These Are the Days of Our Lives" | Queen |
| 26 December |