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The promise to pay the bearer on notes still has some relevance. The Bank of England will exchange the no longer current five pound note you find down the back of the sofa for a current one.
The same isn't true for a round pound coin, the Royal Mint doesn't have to that for a 12-sided one. Apparently you can still exchange round pounds via a high street bank but I'm not sure about large 50ps etc.
Sterling isn't backed by gold reserves anymore so "promise to pay the bearer" is no longer relevant. (As far as I understand anyway)