Albeit it was a few years ago now, but we "broke" our journey overnight in London by staying at a hearby Heathrow hotel rather than risk missing the last flight up to Aberdeen if the flight was running late. Our luggage was kept at LHR and was on the plane the next day - they said as long as your transit flight is wthin 24 hours of your departure time [NYC for us] then we didn't need to pick up our luggage/recheck in the next day.

The last time I transited at LHR in 2021, when you come off the international flight, once you clear immigration you can leave the airport at that point [obviously as long as you are okay visa wise]. Then when you come back, you clear security like you'd need to do if you were transiting immediately given you've got a ticket for your forward journey.