The problem with fitting 20 inch wheels to your Z4 is that to keep your rolling radius as close to the originals as possible you would have to fit tyres with alot lower profile. For example on the rears you would have to fit a tyre say 255/25/20
With a section height that low you would suffer the consequenses of a very hard ride and possible wheel damage from roads in the UK.
I'm running on 265/30/19 and that in my humble opinion is low enough.
The section height is, in basic terms, the distance between the wheel rim and the contact point of the tyre on the road.
With a section height that small, if you hit a pot hole there is very little tyre depth to protect the actual wheel rim from damage or the tyre from sustaining a puncture,
To confirm dave the wheelnut's opinion I too run 235/35x19 front and 265/30x19 rears and on a recent trip to the UK suffered rim damage, be it slight to a wheel rim due to a brocken road surface while driving on the A27 between Brighton and Portsmouth. As DtW says an increase in rim diameter means a reduction in sidewall height to maintain the overall diameter/rolling circumfrance of the wheel thus increasing the possibilty of an experience similar to mine. Maintaining the same sidewall aspect ratio while increasing the rim diameter will increase the overall diameter of the wheel and thus the gearing.
That's about as clear as mud...............