This was the first I had heard of it, but Pseuds' Corner and Home of the Frustrated Hack has an account of it. The incident took place before the FA Cup semi final between Spurs and Wolves:
Tragedy did not follow that day because, unlike in 1989, the police reacted in time.
in 1981 Spurs played Wolves in an FA Cup Semi Final at Hillsborough, and Spurs fans, like Liverpool fans eight years later, were allocated the now notorious Leppings Lane end.
Spurs fans, like Liverpool fans that went after them, felt that the ends were badly allocated. Leppings Lane was perceived to be the smaller end and should thus have been given to the team with the smaller travelling support. But this was probably just perception, and switching ends would sadly just have switched the suffering from one bunch of fans to another.
Spurs fans were sent through the concourses that led to the various pens behind the goal. And those directly behind the goal were the most popular. So just as pens 3 and 4 filled to dangerous levels in 1989, the same part of the ground filled dangerously quickly in 1981.
People were crushed not because of surging support or bad behaviour, but simply because the spaces between the large metal fences were too small. Indeed there was a feeling even before then, without benefit of hindsight, that the supposed capacity of Leppings Lane was overstated and unsafe.