That one is pretty good. The cables and housings have been replaced. The three speed shifter and cable rig is a replacement as well. Shifter cable routing for that era should be along the top tube to a pulley, then to the indicator spindle/chain at the axle running roughly parallel to the seat stay.
Correct shifter depends on the year of the bike. The quadrant was common until about 1948, then correct shifter would be the non-window silver face "upside down" type, then to the more common upside down type of the very early 1950s. The New World used quadrant shifters later than most English bikes did, but the New World also eventually went to a click shifter about 1948. Saddle is a replacement, but it might be OK for your riding style. A B66 would be more appropriate usually.
But what you have is better than most when they show up. It shouldn't be overly difficult to fix the little stuff that's left for you to do. Good find. It's a post-war New World in nice shape.