So this morning I walked to the local Hobbycraft store and bought some Denim needles along with some double sided tape (for fitting the UV strip on the Jib sail).
The Denim needles were a revelation, scything through the mainsail material. They made it so easy the repairs to the mainsail are all done.
All the thread ends are tied off, so no chance of unravelling.
Next step is the Jib. I bought some blue Dacron for a UV strip the last time I stitched the Jib a couple of years ago, but never got round to using it. This time the ease at which the Denim needles are working means I should be able to sort things this week with luck.
I need a stitch ripper to remove the remains of the old UV strip and the rotten stitching, then I can apply the new Dacron with double sided tape to hold it in place temporarily while I stitch it. There's a thin strip around the edge of the leech that has had it too, having split into several parts. I'll apply the UV strip to tuck round the edge and doing two jobs at the same time.
Once it's all stitched, I'll give the sail a wash. At the moment I reckon washing it will to more harm than good, it's that bad.