The government and regulators in the United Kingdom (UK) published several papers on their proposed regulatory regime for cryptoassets — Phase 1 covers fiat-backed stablecoins.
Proposed regulatory perimeter
A summary of the proposed UK regulatory perimeter to regulate activities relating to stablecoins and other cryptoassets is available in this handy two-page document:

Links to HMT, FCA, BoE and PRA papers
a) HMT’s Update on plans for the regulation of fiat-backed stablecoins – 30 October 2023 (link);
b) FCA’s Discussion Paper 23/4 – Regulating crypto assets Phase 1: Fiat-backed stablecoins – 6 November 2023 (link);
c) BoE’s Discussion Paper on the proposed regime for systemic payment systems using stablecoins and related providers – 6 November 2023 (link);
d) PRA’s Dear CEO letter to deposit-takers on innovations in using digital money, including e-money and regulated stablecoins – 6 November 2023 (link); and
e) BoE-PRA-FCA: Cross-authority roadmap on innovation in payments – 6 November 2023 (link).