Euro#1 also seems to have the distinction of being one of (if not the first) Sport models. I think perhaps the USA assembly group produced USA CAR #502 as the first USA sport and at a similar time the UK shop put together Euro#1 as the first European sport model.
Both USA#502 and Euro#0001 had "exhibition duty" being used in photo ops and something for people to drool over in the showrooms. It may have been unclear (at the time) what the eventual disposition of those cars would be... Maybe Tesla wasn't even sure if they would eventually sell them, but ended up doing so.
When a manufacturer sells a demo car, it sort-of shows up as "new" because the first customer bought it from the manufacturer and it was the first time it was registered (since running on reusable dealer/manufacturer plates doesn't require registration.) but in effect is is a heavily used vehicle at that point.
I think some people referred to it as "The first Sport" rather than "The first Sig250", so its' place in history is a little vague that way. I don't think it is too much of a stretch to say that Sig250#2 was the "first official European customer car", and Euro#0001 could be viewed as a marketing car (like what they used to call the "VPs" back in 2008.)
It would have made more sense if they had built #0001 as a VP (V in the VIN) instead of using a regular production VIN for it.
On a side note, I think perhaps Sig250#2 also sat in the London showroom for a little while before being picked up and registered by the buyer. My guess is that they weren't ready to pick up the car right away even though they had pre-ordered it. Maybe they let the London showroom hang onto it for a while as a display car as a favor to Tesla? Did it ever get registered with the T33SLA plates we saw in those first pictures? Were those even real plates? It is being offered for sale now with standard issue sequential plates.