In the end I went to a local repair shop (W Hart Cars at Swallows Cross Farm near Doddinghurst).
He checked over both sills and replaced corroded metal in the outer sill and bottom of the rear arches, removed some surface rust from the inner surface, and injected rust preventative inside the sills. The driver's side had already been patched once shortly before I acquired the car while the n/s was original.
The whole job took 2.5 days and cost a reasonable (I think) £480 including VAT for what looks like a very thorough and tidy job. I'll be interested to see how it fares but am pleased with the outcome.