It takes about 6 weeks from completing production to being ready for delivery at West Drayton.
The large majority of that is getting from the Fremont factory to the Tilburg final assembly plant.
It's hard to be sure because the dashboard can be quite inaccurate, and it doesn't distinguish the various stages. From what I've been told by my DS etc, and heard from others, I'd say it takes 3 weeks from completing production to getting on to the boat on the East Coast (i.e. to travel across the country, get all its customs and other paperwork done, and get onto the ship, plus this stage may also cover quality control and road testing at the plant - your car will probably arrive with around 15 miles on the clock from being tested on the factory's private track). Then 2 weeks or so to cross the Atlantic, arrive at Rotterdam and get to Tilburg, a couple of days there for final assembly, and a couple of days to come across to the UK (by road car transporter).
That's all pretty speculative. The point that your DS will become confident about your final delivery date is the point that the car is "on the water" i.e. somewhere in the Atlantic. My delivery appointment was booked at that point, and they hit it exactly, three weeks later.
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P.S. Production itself takes 2 days if there are no issues (or longer if quality control spots something that needs doing again). It's by far the shortest step in the whole process.