Totally unclear, but there may be some lesser-known channel, or perhaps it's essentially just a form of corruption? Somewhere at the English Emissary in Iran (or the Iranian Emissary in England) could perhaps have physical access to the passport printing hardware and/or stamps. They could be cranking them out as "British protected person" or whatnot. Such dubious passports might get flagged as fraudulent before long, but maybe they only really need them to work until they fly to where they want to be.

"The Iranian officials have also been trying to acquire Swiss and Canadian passports, according to the report." So they may be trying everything and somehow the British passport avenue the one that's actually working out for some reason (Assuming the report is even slightly accurate).