The film, which sees Cohen play Wadiyan tyrant Admiral General Aladeen, pulls in an impressive £4.9 million to end Avengers's three-week reign at the chart summit.
Johnny Depp and Tim Burton's Dark Shadows holds its spot at number three, while American Pie: Reunion falls down two spots to number four.
Gareth Evans's martial arts action epic The Raid debuts at number five with £417,596 from 297 locations.
Elsewhere, the chart sees a re-entry from Aardman's The Pirates! at number nine. The Hugh Grant-voiced 3D animation sees a 4% climb in ticket sales to leap back into the top ten.
The UK box office top ten in full:
1. (-) The Dictator - £4,963,745
2. (1) Avengers Assemble - £2,814,216
3. (3) Dark Shadows - £1,638,651
4. (2) American Pie: Reunion - £1,372,896
5. (-) The Raid - £417,596
6. (5) Beauty and the Beast 3D - £395,660
7. (4) The Lucky One - £252,447
8. (7) Salmon Fishing in the Yemen - £167,171
9. (11) The Pirates! In an Adventure with Scientists - £132,235
10. (6) Safe - £121,399
Watch Digital Spy's exclusive clip from The Dictator below: