It should be the same for your 2004 as in the video. The top edge pulls away while the bottom edge swivels - pull on the top edge towards you as you sit in the seat. When the top releases, the panel will swivel down like the glove box door - then you can pull it off.

Sorry for the delay, I've actually tried to take this apart however with no luck.
I was able to remove the upper and lower steering cover but I couldn't see much. In order to have a complete view I need to remove the knee panel underneath. But I couldn't find the way!  it seems there are no screws anywhere and the only info I found online says to simply pull downward until it come off ( this video https://www.youtube.com/watch?v=gtNnLPalEpE) but I really couldn't do as I'm pretti sure something was going to crack, my panel is also a bit different so it might not be the same model ( mine has a little selector to adjust the headlamp height and some sort of mini glovebox, but without any cap or hinge, is just a hole in the panel).
Any idea on how to take this off?

Thanks Dan, I deleted the link.

Ken

VivianFulton appears to be a scammer. Be careful with the link.

Let us know how you fixed this issue!

+1 - what Dan said...

Being a modern car, the interior (cabin) portion of the steering column would be separate but connected to the lower portion that connects to the steering gear. Most likely there are flexible joints and a compressible (telescoping) section to keep the driver from being impaled in a collision. Since yours an tilt, it will certainly have flexible joints (universal joint or similar). 
The cabin portion will be bolted to the dash structure for support. That is where your side-play most likely is occurring. It wouldn't take much bolt looseness to allow the assembly to shift on its mounting. You may also be able to detect a slight up/down play with the tilt locked, though the bolts would have to be slack by a thread or two for this to happen.

Remove the plastic covers and tighten any bolts you see.

I've seens videos about other cars having the same problem fixed by tighten some loose bolt inside the steering column. However, I cannot find a specific video for the mini, I don't' know which are the bolt that needed to be tight, I've seen video only on how to disassemble it and it seems quite complicated (remove the airbag, then the wheel, then the column cover).

It has 93k miles.

How many miles? There could be worn out inner or outer tie rod
ends, or other basic suspension parts.

Hello All,
I've just purchased a used 2004 mini and I've noticed an issue with the steering wheel / steering column.
Basically if I apply a bit of force I am able to move the steering wheel left and right, lets say by 1 cm. I am not sure if the movement comes from the wheel or from the column as the latter is covered, but from what I see from videos if the steering wheel was loose then it should tilt not moving. The movement happen even if the car is parked with the engine off, so the problem is not related to wheel bearing wearing. When driving it happens quite rarely that you move the wheel, so I wouldn't say its dangerous but is quite annoying.
Any idea on what it could be? How to fix it?

Thanks.