It can go all the way through. It wouldn't surprise me if the NAP agent thinks you are mad to leave it overnight in LGW, but by 10 minutes you are inside the requisite deadline and it's a perfectly sensible thing to do. If you are staying in a hotel near LGW you have another unusual option, you can retrieve the bag in LGW, take it to the hotel to get whatever you need there, then re-check the back between about 16:00 hrs to 21:00 hrs in the pre-check service that LGW offers.