Unfortunately, the bolts came loose again so ordered the replacement parts direct from BMW (32311157967). These were only about £5 for the pair.
Now that I had identified where the play was, there was actually no need to take the steering wheel off, just the plastic shrouding on the steering column. This involves unscrewing the Philips head screw and using a plastic pry tool to release the shrouding (same as what is being done at 08:20 in the video below, but with the steering wheel still on):
https://www.youtube.com/watch?v=K00JRcr7Ivk&t=497s
Should look like this:
Next remove the two small Philips head screws that hold the alarm motion sensor in.
With all that out of the way, you should be able to see the anti tamper bolts. I recorded a video of them, showing the movement I was experiencing.
To remove the bolts, you can see I etched some marks into the side of the head of the bolts, and used these for purchase to loosen them with a flat head screwdriver (by pushing the flat head into the grooves to rotate the bolt).
I removed the first bolt and replaced it with the new one before untightening the next one. This ensured the column stayed in place.
To tighten the new bolts, I used an E7 (female Torx) attachment to a ratchet. Note that you might find there isn't enough clearance above the bolt - if this is the case, ensure that you have adjusted the steering column to its position closest to your knees.
Tighten them until the heads sheer off.
With the bolts properly fitted, it's just a case of reattaching the alarm sensor and putting the plastic shrouding back on.
EDIT OVER - Original Post Below
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There have have been a few posts on fixing play in the steering column, but all I have seen relate to play in the steering (i.e. dead spots) rather than in the actual column itself.
I'd noticed that when pulling on the steering wheel across all 4 axis, there was play in it, especially up - down. I am talking about 5mm or so, enough to notice the column was moving.
Initially I had hoped this would be solved by replacing the track rod ends and wishbones (on the basis it's all connected, and had been advised there was slight play in the bushes), but although the steering was much tighter after replacement, the movement in the column was still there.
I then had the Torx bolts in the universal joints tightened - item 3 below - but again although this improved response, the play was still there.
With a free afternoon, I decided I would investigate. I used this video, starting from 07:00, to disassemble the wheel.
NOTE: The video doesn't mention it, but you MUST disconnect the car battery before proceeding. Otherwise you risk getting an airbag warning light (I can't confirm if that is the case since I disconnected the battery).
https://www.youtube.com/watch?v=K00JRcr7Ivk&t=514s
I found that after removing the plastic around the wheel (around the 08:36 mark), I could see that the anti-tamper bolts were loose (circled red below). These connect the steering wheel assembly to the steering column.
These are item 15 below, part number 32311157967
Being anti-tamper, they don't have heads (the heads sheer off when you install them), but I found that using a chisel I could introduce a wedge into the side of the heads, which I could in turn use as purchase with a flat head screwdriver.
This entirely solved the problem, and now the steering wheel/column is completely still when pulling on it.
I imagine the bolts had come loose over the years from drivers holding onto the wheel as they get in/out due to the low ride height.
Final steps were to reassemble, reconnect the battery and set the clock.
If the bolts come loose again I will replace them, but am hoping this works for now.
