I don't think anyone could credibly claim that Bitcoin is what it set out to be. The original paper calls it "electronic cash" and in its introduction describes private people using it for small transactions, replacing trust with cryptography. I would hope that a CBDC shares that original goal of replacing cash, though to what extent cryptography will be involved I'm not sure. (I do doubt BoE are just going to fork the Bitcoin code and spin up their own blockchain.)