Mesozoic
Reports tend to take 7-10 days, don't wait for the report if would mean that the request is late, you can always say in your request that you will be sending additional information once your receive the ESA85 and the DWP should give you an additional four weeks from the date of your letter for you to do this.
If you do have to do this, call the DWP once they should have reasonably received your letter to check that the extra time has been recorded on your file.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems