Check how much the outer cables compress when you pull on the brake. If there is not a brand name on the cable outer it is probably cutprice rubbish. Consider making up new outers using a quality outer cable.
If the levers don’t have Sturmey-Archer written on them, they are probably some cheap junk fitted to keep the price down (considering the bike’s origins).
Fortunately proper S-A levers are inexpensive so it could be an easy fix. About £9 each from SJS, but your lbs can get them for you.
Also Avid make a lever with adjustable pull. I have used them successfully, but I think the S-A levers are more rigid.
If you could post up some pics of the brakes, levers etc it would help.
Edit:
One thing I didn’t cover is that these brakes last almost forever, but a corollary is that they need extensive bedding in. So, if the bike is new, just go out and use the brakes hard, drag them when going down hills etc.
Even when perfect they have a different feel to disks, far more modulation, and less put your bike on its nose feel for the same stopping distance. (Modulation is one reason I like them, I use them a lot in loose or slippery conditions).