Resting the camera on the dashboard of the car to keep it relatively stable would be a good approach. Then it's just the car's movement and the cars outside that will create the blur and not camera shake. This will have to be experimental as far as shutter speeds and exposure are concerned. Obviously night time would work best if I am going to record light streaks. The camera pointing at back seat and kids with blur outside?
Big Ben and houses of parliament Depth of Field being used creatively - I feel this gives a much better effect than having shot the image with a smaller aperture which would give a bigger focus in the image (so Big Ben in the background would have been in focus too).