(This is a problem I ran into that took my mechanic and I a little while to figure out, and which despite reading a lot of great threads here I wasn't able to find a solution to. So this is a record for anyone who happens to run into the same problem in future, with the solution as a reply below. I've tried to cram it with as many key phrases I searched with before, so it's a bit wordy, sorry. Also, I've probably got the order of events slightly wrong.)
I've got a 1993 Rio, with a HIF38 carb, electronic distributor. After having a frontend suspension rebuild, new clutch kit, and some oil seals replaced (including fuel pump seal), the car ran fine for several weeks of usage around town.
Then I went on a longer trip into Wales, and soon after getting up to 70mph on the motorway, the engine started stuttering/misfiring, and rapidly lost power. I shifted down through the gears, keeping the revs up, but no power so quickly pulled over, before stalling out.
Checked the new-ish fuel filter between pump and carb, no scary debris, some fuel present.
Temperature was fine, was able to restart and idle fine, revving high in neutral also seemed fine. Yet trying to pull away rapidly reproduced the problem at low speed. Waited for recovery, everything checked over. AA guy backs off the fuel mix a quarter turn. All seems fine and car behaves itself at a steady 60mph, before getting stuck in traffic and crawling for a few miles - despite rising engine temp, everything is still fine.
Carry on with the journey, but shortly after run into the same problem on a long climbing dual carriageway in Wales. Abandon the trip, get towed home.
At this point I thought it could be ignition related, or over/under-fueling (though no signs of fuel overflowing the carb, and the float had been replaced recently). Replaced the coil and HT leads, checked all the LT cabling and voltages too, nothing unusual found.
Went out again on the same route, same problem on the same hill climb. Bit more patient this time, so sit with the engine off for a while, then set off again keeping the speed down. Get home no problems.
Research suggests fuel vapourisation caused by a missing spacer, but says mechanical fuel pumps themselves either work or they don't.
My mechanic checked the fuel pump spacer was still present, and also checked the pump was functioning when going up through the rev range. Fuel gets consistent squirted into a jam jar on the output side of the pump. Seems fine.
As the problem only occurs under the highest fuel loading (hill climbing at speed), I'm still thinking fuel starvation somehow. Several hours on the motorway at 60mph, no problem. Yet I could force the problem by getting revs over 3500 for any amount of time - guaranteed power loss and having to stop after a very short period of time. Could there be a bit of a vacuum forming in the fuel line?
I rarely fill the tank and had been avoiding it just in case, but after a long drive absentmindedly filled the tank completely. Car conked out after just 10 minutes of doing 30-40mph. Maybe a full tank suffers worse?
I started checking for a vacuum in the tank by listening for a hiss when opening the vented fuel cap. Possibly heard something so replaced the cap in case it was blocked - no improvement. My tank doesn't have an open vent hose through the boot floor, instead it is attached to a charcoal canister in the wing. The canister is no longer attached properly with vacuum hoses or to the breathers or carb, maybe it's blocked?
I have the tank breather hose, non-return valve, breather pipe to canister, and fuel line checked for proper flow - no problems found, so isn't fuel starvation due to vacuum.
Back to my mechanic for the final diagnostic and solution - see my next reply!