Current reactors (light and heavy water reactors) all use solid fuel, which is very inefficient due to use of once-through fuel cycle.

Because xenon is the most common fission product, and it's a gas, the reaction must be stopped before all fuel is used, as otherwise the solid fuel pellets would crack. If you assume 3% enriched uranium (U-235) and 97% depleted uranium (U-238) (a typical fuel load), the fuel pellets are unusable after about 1/3 of enriched uranium is spent. So the fuel is removed and "thrown away" while it still has 2% U-235 in it.

Switching to liquid fuel reactors assuming no other changes would immediately increase supply 3 times (because xenon simply bubbles out). Switching to liquid fuel breeder reactors ~ 100 times. Switching to breeders based on thorium - around 1000 to 10000 times.

Peak uranium is only a problem because we're using a very inefficient nuclear reactor technology - water reactors. Why? Because they were chosen by the military and the technology/know-how was already there. Efficiency was really low on the military's list of priorities.