[McMurdo]

We had the Belling Classic Super 50, a WHich? Best Buy, 1964. Never had to replace any element or simmerstat, just the Smiths timer.
DO make sure power is getting to the element before condemning one. They knew how to make them in those days unlike the rubbish elements you get these days that sometimes last a couple of dishes before going open.
I'm not sure if yours is the same but on ours, 3 of the rings were on simmerstats and the fourth on a thermostat with spring loaded sensor in the middle that touched the pan.

I assume you've looked at the connections in the switch cabinet, they're often solid wires in this age of cooker, twisted and looped around a screw terminal that can work free in time.