Kiwi, the transition altitude is 3000' (in the UK, outside controlled airspace). That's the only thing that's defined. The transition level is the first usable FL above the transition altitude. This implies that, depending on the exact QNH, the transition layer can be anywhere between 0' and 499' thick.
But yes, the transition altitude varies by country. And in the UK, there are bits of controlled airspace that have a TA of 6000' even. In the Netherlands, it's 3000 for IFR, 3500 for VFR. In the USA it's 18.000'. Different countries have different considerations as to where they put the TA. Geography (mountains or not) does play a part in that. In the Netherlands for instance, there's not a lot of terrain that rises to 3000'. In fact, you'd be hard pressed to find terrain here significantly higher than 1000', so a TA of 3000' works fine for us.
Europe is trying to harmonize the TA, but as with all things European, this takes time.
And while most of the rest of the world has standardized on a semi-circular rule (VFR: odd thousands + 500' anywhere between 0 and 180, even thousands + 500' anywhere between 180 and 360) or a variant thereof, the UK still uses a quandrantal rule (odd thousands 0-90 degrees, odd thousands + 500' 90-180, even thousands 180-270, even thousands + 500' 270-360).
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