which you do not need if the passport is issued in UK
Ah, right, so the letter is not a requirement to confirm that the passport is real, as you claimed, it is just a letter requesting IB's cooperation with transferring the visa/extension to the new document.
Passports issued through HMPO, The Trendy, are issued in the UK ("Issued by: HMPO"). There is nothing on the passport to suggest to Immigration, or anyone else, that the passport was not issued in the UK.