I had the chance to get under the car today and have a look around.
Basically I saw steering gear, load of pulleys, belts and pipes, all of which looked expensive, none of which I was happy to leave exposed to the elements, dirt, grit, road salt and stones that they may have come into contact with.
I refitted the plastic part to the underside of the radiator (it was much easier at home than by the side of a busy road).
BMW quoted me £118 for a new plastic undertray so I decided to refit my own, which although a little scuffed wasn't too badly damaged.
I re-used the 4 remaining original "twist-fit" screws and sockets at the back and on one side after cleaning them up with WD40 and making sure they would do up tightly, then drilled a few holes into the plastic along one side and under the bumper and secured it with a few large cable ties.
I feel happier now the protective shield is (even more) securely back in place.