Well, I tried the SCART-to-HDMI upscalers but, although they worked, the resulting picture was rather artificial. I also found that they became very hot when left on for an extended period.
However, the TV has an AV1 RGB SCART socket and an AV2 component / composite 5/3 socket phono input option. The RGB is fine for Sky SD / DVD - much better than the converted HDMI option, although the composite input isn't up to much, but OK for my old VHS tapes.
So my advice to anyone else thinking of using SCART-to-HDMI converters is only to do so if there's no other option.
I do wish that the Panasonic picture was a little brighter though...