The answer to this question
came from Mishna Berura 426:3 which defines the light from the moon on which one can make the blessing as follows:
ג) ונהנין מאורה - דהיינו בעת שזריחתה ניכרת ע"ג קרקע. אם נתכסה הלבנה בעבים אם העב דק וקלוש שנראית הלבנה ממנו ונהנה בה מברך ואם הענן עב אינו מברך
3) to benefit from the light. That is that when the moon shines, the light should be noticeable on the ground. If the moon is covered with thin cloud so it can still be seen and noticed on the ground, one can make the blessing and if not one cannot make the blessing.
When there is other light (e.g. street lights) also there, I might think that I would need a higher intensity of moonlight for it to be noticeable and hence to make the blessing. Or one could say that the blessing is fixed on the brightness in the absence of other illumination.
Have our Poskim spoken about this subject?