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Everything I can see online suggests you have to sell the shares and then use the proceeds to buy them back inside the SIPP wrapper. No idea why, maybe it's just so they can track contribution value unambiguously.
One question about the shares I didn't see mentioned: do they pay dividends? If you get a return that's higher than savings rates, it's worth something even if the value isn't going up.
Can open a S&S ISA with someone like Vanguard. Fees are minimal (0.15%) and it’s straightforward