No, the shade isnt threaded. And the 'collar' is surely going to be just a cylinder or tube open at both ends with a female thread at one end and a male at the other. I suppose it is possible that if the plastic part was positioned where I think it was positioned, it would have been constantly heated up and may have become brittle? But when the shade hit the roof of the cab and came off, my wife says she emphatically did look to see if a part had come off. She didnt see any part, - much less two parts!

The part which doesn't fit seems to be called an UNO RING. There is one on the Amazon link but the ones showing on the electrical fitments seem to have a longer 'cylinder' under it. I just cant figure out why on earth the original one SUDDENLY after that taxi ride isn't long enough??

Could you post a picture on some image sharing site and post the url
here?

And maybe a drawing by you of the missing part.