Following pictures and diagrams from M0UKD, I've built up a 9:1 impedance transformer sometimes called an Unun.
This transformer meant that a random wire strung up on the balcony could be quite easily tuned up and achieved a 1.1:1 SWR without too much trouble.
I guess the name Unun is an adaption of Balun which is balanced to unbalanced whereas this is unbalanced to unbalanced.
Here it is all boxed up. My thanks to Stephen, VK2BLQ, for the loan of his excellent drill press.
As a test, I hung out only a few meters of wire with a short counterpoise and the antenna analyser looked pretty good near 28MHz.
My plan is to get on air with this tomorrow night for the home brew group net.