I found the reason why the car had dumped all the coolant on the road.

When I put fresh water into the radiator to see where it was coming out, I found a small stub of a metal pipe at the back of the engine that had been covered with a rubber cap tied on tight with a jubilee clip.

I've now put this cap back on nice and tightly, refilled and since had no problems.

Presumably, if this cap was in the process of coming off it would not have allowed the cooling system to pressurise properly and hence cause overheating.

The real puzzle though is what is that pipe doing there in the first place. It seems to serve no purpose except to give the coolant somewhere else to escape from.
I'm still in denial about the BHG.....

that pipe is a part of the cooling system. Its a part of the piping that routes from the thermostat housing back around the engine to the intake manifold.

That pipe is for LHD and RHD depending on which one it was installed in for the heater hose and the other side is capped off. Another way of saving money by making parts universal and making another trouble spot.

My 86.5 did the same thing and I always wondered why that stupid thing was back there. I just took a metal cap and braized it on there then never had to worry about it again. The motor that I took out of my 87 had a peice of hose with a spark plug stuck in it and a couple hose clamps when I bought it. The only thing that is going to suck is the coolant gets down into the exhaust cover below it and it will burn that crap for days.

This EXACT thing happened to me a half an hour after I bought my Supra, and began driving it home! All of a sudden the temp redlined and I had to pull over. I could smell burning antifreeze, and see it on the exhaust cover. I drove it for five more minutes, to a rest stop (thankfully it was right there, I was out in the boonies at 12 am). I hitched a ride back home (2.5 hours...) from some random dude, and drove back up there with some friends the next day.
It was that damn cap at the back of the engine, clipped tight, and cracked open. I couldn't figure out what it's purpose was, but I knew it was the problem. I rigged up a new rubber thing and clamp, and I haven't had any problems since, although I check it from time to time to make sure it's on tight.