The last official Home Video release of The Burning in the UK was from Thorn/EMI (they were horrified, at the time, that one of their titles had made the nasty list), so no idea who'd hold the rights now. As far as I know Vipco never officially had the rights, so don't look at them for answers.
But when Dragon tried to release it on the continent, MGM stepped in, so maybe MGM DO still hold the rights here.