Indeed, that situation can be very tricky. The obvious thing to keep in mind -- which you no doubt know well -- is that the angle of incidence equals the angle of reflection. If the light is coming in at 45º it will bounce off at 45º in the opposite direction. When the reflective surface is flat, you can usually place lighting units so that the camera does not see the reflection of the unit. But when the surface is curved, the task can be enormous. Well-placed flags often save the day. Black wrap is also useful, Sometimes wrapping c-stands and light-stands with duvetine also helps remove unwanted gleams of reflection.
A slightly different and probably easier approach is to use very large soft lights. There are special rigs DPs use to light cars which are essentially huge soft boxes longer than the car itself, which is how they get those excellent highlights along the folds of sheet metal. Several 4x8 white foamcore sheets strategically placed end to end, illuminated with roughly equal intensity by floor lamps whose own reflection is blocked by duvetine or black foamcore can, with a lot of work, emulate such a look. Or else overhead space lights or "chicken coops" through a giant silk.
I suggest you make sure your client understands that all this takes time, time, time, and crew, plus grip and electric equipment, to do right.
Many thanks, it's the direction I thought I should head in. Good news is we now have a rig day to experiment with and the BBC have left some space lights up that I can use. Hopefully by the end of tomorrow things will be in good shape.