I read the other feedback on this site to gain confidence that I was ordering the right part (ES 1083371) for my trimmer, and indeed it is the correct diameter. It arrived within a couple of days, and I have just completed the fitting.
I first tried to fit it from outside to inside, but I couldn't get hold of the small tapered tongue inside the tank, even with surgical tongs. I then resorted to feeding a small diameter wire (about half the ID of the tubing) through the small hole in the tank from outside to inside until it protruded from the tank filler cap hole.
I then slid the tapered end of the tubing along this guide wire from the tank filler cap side and wiggled the wire in the through-wall hole whilst gently pushing and twisting on the tubing going into the tank. When about 3mm of the tapered tube was visible on the outside, I withdrew the guide wire and gripped this small tongue in a pair of needle-nosed pliers and gently pulled about one inch of tubing through the hole. It is much easier to get hold of the tapered end on the outside of the tank.
When I had pulled enough tubing outside to hold firmly in my fingers, I put slightly less tension onto the other end of the tube, and by stretching it on the feeding side, the diameter was reduced so that it passed more easily through the hole. I was then just left with deciding on how much tube to have outside and inside the tank. The old tube was used as a guide for the inside length since it had a distinctly narrowed diameter where it had been held in the tank wall.
I was able to push-fit the tube onto the stone and carburettor pipes with moderate effort, and the tube is a good tight fit on both. It is also held well in the tank wall when the tension is removed.
I have not yet tested the trimmer as I don't want any 2-stroke fuel left in it over the winter, but I don't see why I should encounter any further problems when I do come to use it in the spring.
It might be possible to get another two replacement lengths from what remains of the tubing, but I have certainly used less than half of the supplied tube for this first renewal.
In summary, it is the correct tubing for my strimmer, it was shipped quickly, it is a DIY task to fit it, it will do at least two replacements so it is good value, and was un-obtainable wherever else I tried to buy it.
Thoroughly recommended supplier, and goods fit for purpose.