I remember seeing the shielded cables in older gear but would you call that coax as we know it today? it appears modern suppliers still call it shielded cable.
By coax I mean specifically the flexible controlled impedance stuff for RF that at this stage seems to have arrived in/around 1936/37 and discounting the solid/hard tube type that was around before then.
John's post #4 with the picture of the 'Television screened feeder cable' must be some of the very first coax of the modern style.
As the grey cells rapidly progress towards their use by date, I'm finding what everybody has posted very interesting and thank you all for it, it brings back long lost fleeting memories of all sorts of things.