Some Help?
The center part that unscrews does so in order that you can adjust the steering wheel in and out. Unscrewing it loosens the "lock" and screwing it tightens it up so the wheel will not move.
Yes, the padded part (but NOT the hard, black plastic) comes off. Grasp it by the chrome ring and pull it away from the black plastic. Behind it you will see a bolt holding the black plastic piece to the end of the steering column. Remove that nut and you can remove the plastic adjuster piece. HINT: Tighten the steering wheel adjust before you remove anything. Otherwise, the adjustment dohickey (technical term) inside the steering column might slip down inside and it can be a pain the butt to retrieve.
Attached are two snapshots from the workshop manual. The first is of the steering wheel. Note that it shows part 11, which actually is in two pieces - the outer padded section and the hard, black plastic piece. It is called the steering wheel adjusting nut.
The other snapshot is of the steering column, to give you a better idea about all the parts in it and so you can see the hardware that allows the steering wheel to be adjusted and locked into place.
If you haven't already obtained them, might I suggest you look into getting some of the manuals you will need to help you work on your car? There are 3, all available on CD on eBay. (Sometimes the same CD will have more than one.) First is the Sunbeam workshop manual for Tigers. Then there is the Sunbeam Alpine Parts Manual. Be sure that one covers Series V Alpines. And the third is the Sunbeam "260" and "289" Parts Supplement, which supplements the Alpine manual. Since many of the Alpine parts were used on Tigers, Rootes only published a supplement parts manual for the Tiger.
And, no, I have nothing to do with the CDs available on eBay.
Good Luck!