Seatbelts don't last forever. In fact, some racing organizations recommend replacing them every two years. Sun and abrasion can take a toll. If you want to maintain the vintage look of your 70's Mini you might appreciate these non-retractable shoulder belt kits. Adjustments are made by cinching the belt through the chrome buckles, just like the old days, and yes, the loose end falls between the seats. Sold each.
See also SAC0196 for belts with center attachment stalk.