The advice to seek some sort of authority to travel from the British Embassy is incorrect and has been for a very long time. They will only direct you to the entry clearance section of the gov.uk website for advice.
The ability of UK border or airline liaison officials to take local pragmatic decisions on cases like this and allow the OP to travel has largely been taken away from them by ever more prescriptive rules and official guidance in the last few years.
‘If I was the OP I would get my passport back from whichever embassy it is at and have it couriered to him to allow travel back to the UK.