That photo shows a pretty filthy bike.
I'd start with a full disassemble of the rear brake caliper, and clean all the metal parts, and especially on the friction areas. Then I'd buff the whole thing with brasso or JIF cleaner. Then reassemble and see if it improves. If not, you could rough up the friction surface under the quick release using some sand paper.
If the main spring in the brake caliper is weak then this may be a losing battle, because sourcing replacement parts is hard. In this case, just explore for some more modern double pivot calipers, and fit them up with new brake cables.
The temp fixes suggested by others are exactly that - temp fixes. I wouldn't even ride this bike if your braking ability is compromised.