Rear Wheel Lock-up Mystery

[T4tomo]

Something damaged in the freehub?

This was my thought too. although when a free hub fails you often end up pedalling but not moving forwards, i.e it fails to engage, I'm guessing jamming could also occur.

easiest way to tell is to stick in a rear wheel off another bike

 

[Ajax Bay]

What happened was that the bike came to a dead halt in the road. I got off, had a look, couldn't find anything obviously wrong, got back on the bike and carried on cycling, only to have the experience repeated again. . . again. . . and again. . . . new chain and cogset, . . . a new back wheel, . . . the shop whose friendly staff suggested that the problem could be due to the rear wheel's skewer shifting under pressure, causing the tyre to rub against one of the frame's rear stays. At any rate, they replaced the (temp) QR skewer with a nutted one, and there has been a mild improvement.
Nevertheless, the problem still persists; that's to say the bike 'locks up' when I'm cycling uphill in bottom (20") gear . .

I worked out what the problem was and did up the QR.
It's not going to be chainsuck - that will lock the cranks, but not the rear wheel (it won't happen on fixed).
It also normally leaves the chain jammed between chainrings and chainstay, so it's obvious what the problem is.

OP is not saying the rear wheel locks up, they're saying "the bike [comes] to a dead halt" and that the "bike locks up" even with a nutted axle. As a 60s/70s bike the dropouts will be horizontal. Old bike, well used OEM? inner chainring, middle chainring needed replacing, new chain. The RD cage spring (keeping some tension on the return section of the chain) may after 50 years be weak. See diagram ^ ^
I agree that normally the result of chain suck would be dirty hands as you unstuck the folded chain in the inner ring/BB shell/chainstay area (and therefore as you say, 'obvious').

easiest way to tell is to stick in a rear wheel off another bike

OP has fitted a new wheel. Problem persists.