Please note that I was wrong about Charles Stanley’s fees: certainly not the lowest.
I’ve now switched my JISA to Vanguard, who do actually have the lowest platform fee that I could find amongst S&S JISA providers. A fixed fee would be better in the long term, but I couldn’t find a fixed fee provider that does JISAs.
Vanguard only offer their own funds to invest in, but there are good, solid choices with low fees to go for. I’ve gone for their US total market tracker.