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Reuters reports Finn died in hospital in Croydon, south of London.
"Mickey had been having health problems for a while," Barry Newby told Reuters.
Newby said Finn was believed to have died of kidney and liver problems, although no official cause of death has been announced.
T.Rex are widely credited with making "glam rock" a mainstream phenomenon with hits like "Get it On (Bang a Gong)," "Hot Love," and "Children of the Revolution."
Originally formed as Tyrannosaurus Rex in 1967 by lead singer Marc Bolan, the band shortened their name in 1970 after Finn joined to replace original member Steve Took.
Although not as popular in North America, the band had a huge following in Britain and sold 39 million albums, according to Rolling Stone.
Bolan, the most famous member of the band, died in a car accident in 1977, former member Took died after choking on a cocktail cherry in 1980, and bassist Steve Currie died while on holiday in 1981.
Finn resurrected the band in 1997 under the name "Mickey Finn's T-Rex," and released the studio album "Renaissance," last year.