Do you have a document or a regulation for such limit?
As stated, individual airport's instructions may have guidance, and if the word 'immediate' is used then that is what is expected (i.e. no stopping if you're moving toward the runway when issued).
From a personal perspective the answer is always immediately. I would never issue the clearance in the expectation that you will take any time to depart, therefore when the clearance is issued you can be rolling. Any time spent not doing so is time wasted on a capacity constrained runway. 99.9% of the time there is someone waiting for you to leave so they can too....