DAVE BEATS FOALS AND DIDO IN UK ALBUM CHART RACE
It was inspired by his brother, who is serving a life sentence for murder.
Over 11 tracks, Dave unflinchingly examines the impact of that conviction and the tough social conditions that confront black working class youths.
Foals were just 279 copies behind with their fifth album Everything Not Saved Will Be Lost Pt 1, while Dido's comeback landed at number three.
According to the Official Charts Company, Psychodrama racked up 26,390 combined sales, with streams making up 79% of the total.
Psychodrama is the first British rap record to reach number one since Stormzy's Gang Signs & Prayer in 2017, and three of its standout tracks also entered the top 40 singles chart.
Disaster, which features Mercury-nominated rapper J Hus (himself currently in jail for carrying a knife), was the week's highest new entry at number eight.
It was followed by the autobiographical Streatham at nine and the more laid-back party anthem Location at 11.
Elsewhere in the singles chart, Scottish singer Lewis Capaldi scored a third week at number one with the heartbreaking ballad Someone You Loved.
Swedish pop star Sigrid saw her defiant single Don't Feel Like Crying jump 14 places to number 20, as the same time as her debut album entered the chart at four.
Teen sensation Billie Eilish scored her third top 40 single in five months as Wish You Were Gay debuted at 26, while Boasty - the all-star collaboration between Wiley, Stefflon Don and Sean Paul - entered the chart at number 33.
In the album chart, Dido's fifth record Still On My Mind was a new entry at number three, with other new entries for Paul Weller's live album Other Aspects (10), Juice Wrld's Death Race For Love (12) and James Morrison's You're Stronger Than You Know (14).