Big con on the offer! I received the offer pack immediately after accepting the offer, but the pre-employment check for me did last long! I think mine has taken about two months! But don’t worry, perhaps it is because I’m an international student and they do have difficulty reaching my high school to verify my A Level equivalent exams. Since you’ll start the job next month, I believe yours will be finished sooner.
Maybe you could just wait for a few days, and if don’t get the offer pack by then, just contact them again and ask. Don’t worry about the pre-employment check, once they decided to hire you, they definitely do not want to lose you since they’ve already invested so much in you!!
Congratulations again! Glad that we’ll be colleagues :))