My car suffers of steering play as well... (+4 / 2006 / 40000 miles) but on closer inspection it seems to originate from the channel where the spacers run/slide along.
I would consider UV-joints a rather non-typical problem. To quickly check the rack you can grab the bracket where the steering rods are joined together and move it vertically up/down. If there is no play/movement, the play may originate from the UV-joints.
In my case, the channel seems be worn out as the tube is made of alloy and the spacer of steel, guess where the wear is. The channel is now about 21.2mm wide (0.8mm wider than the spacer), that is a lot of play. Don't know yet how to solve this, maybe I manufacture sleeve which goes over the spacer to increase the diameter and reduce play.

[Linked Image]
[Linked Image]

Cheers, Peter