Without Allstate, Marty McFly might never have left 1985 or perhaps would have traveled back in time in a Buick, forever disrupting the space-time continuum of the seminal movie trilogy.

With its gullwing doors and nuclear reactor stashed in the boot, the DeLorean sports car may well be the world’s best known time machine. Now the vehicle that sped Marty McFly, played by Michael ...