Raleigh chopper MK4 gear shifter stuck in 3rd, cable moves freely and I can pull it into second

Try turning the cranks with the back wheel lifted up gently as you shift (even backwards will work). These sturmey archer hubs don’t really like shifting when nothing is moving and it feels the same as a cable being jammed. Otherwise; these work in reverse to what you expect, the lower gears are when there is more cable pulled / more tension. So if you can’t get down from 3 to 2 then 3 might be too slack and there isn’t enough pull, try tightening the barrel adjuster near the indicator chain to get more tension on the cable. Perhaps the cable has stretched over time. When you pull it at the hub then cable tension doesn’t matter so that always works.