Some play is to be expected in the Singer steering. In fact, about 4 inches at the steering wheel is normal when the car is fully laiden. When rebuilding the steering box, this translates to about 1″ of play with the box on the bench and about two in an unlaiden chassis.
Before removing the box, check to see if there is any fluid in it. Often there is not, indicating that the seal needs to be renewed. You may find that rather than oil, the box is filled with grease. This is a quick and dirty
solution to a leaky box and not standard practice. It definitely indicates that the seal requires renewal.
Check the Pitman Arm and bushes for play while the box is still on the chassis. This will require an assistant to turn the wheel while you examine the box. First, check to ensure that the arm does not move on the spline. No play is tolerable here. Remove the Top Cover Plate to inspect for play in the top bush. Crawl under the car to check the bottom bush. At this point you can also check the retaining bolt and nut. The retaining bolt is often stretched. Change the bolt if required.
If excessive play is found, the box should be removed and examined as follows.
Examine the Pitman arm for wear along the shaft. Up to .010″ is tolerable. Bushes most likely will require renewal and should be reamed in to make the shaft a tap in fit. Note that the top bush is located with a pin or set screw, so don’t force it in or out before removing this.
You may find some ovality in the Pitman arm Peg. While not usually the source of trouble, this can only be corrected by replacing the peg.
Probably the key source of play is in the Brass Steering Nut. Wear to the outside ends of the nut will lead to play in the housing and requires the nut to be renewed. The steel collet at the top of the nut may also be worn and can be renewed.
Wear to the internal thread of the Brass Nut is the most common cause of play. If the nut can be wobbled on the shaft, it must be replaced. No degree of wobble is acceptable.
The cast steering box housing itself can also wear, especially if fines from the brass nut or steel collet have circulated through the box for any length of time. The box can be resleeved if necessary to correct.
On the steering wheel hub, the tapered keyway can wear. This can be rectified by making a new key, oversized if necessary.
Finally, the felt seal at the bottom of the Pitman Arm should be replaced with a modern lipped seal.