A less common problem is loose or missing cotter pins. Up and down movement of the kingpin relative to the wishbone will again be present because the "eye" of the kingpin has has been worn oversize.
Have an assistant apply the brakes hard. If the movement dissappears the wheel bearings are worn, if not, it's king pin wear. If you can see no movement in the lower kingpin bush, check the "upper outer" shock absorber arm bushes for wear. Also, while the brakes are still applied try and rotate the wheel backwards and forwards. If you get a "floppy" sort of rotation movement, this confirms your "upper outer" shock absorber bushes are worn, and even worse, your shock absorber lever arm may be lose on its shaft. Both of these items need immediate attention, especially if your car is twitchy under brakes.
Check the rubber gaitors on the steering rack and replace these if there are any splits or cracks. If you don't, you will soon be up for a replacement steering rack!
Check wheel studs for stetching, check steering arm to kingpin bolts for tightness.
Gillspeed is a specialist Spridget and MGB supplier (new and 2nd hand parts) and workshop here in Victoria. Bob Gill started Gillspeed back in 1974 and offers overnight service throughout Australia.