If you said "west", you're usually wrong. But today you're correct, just as today is also a rare day when the sun actually rises in the east.
Let me attempt to explain.
The astronomical term for what we're interested in is azimuth, which is the direction of a celestial body from an observer on Earth. It's measured as an angle around the horizon, clockwise from north. Think of it as a compass bearing. North is 0°, East is 90°, South is 180° and West is 270°.
The celestial body in question is the Sun. The azimuth (or direction) of the Sun changes throughout the day, thanks to the rotation of the Earth. In the northern hemisphere it passes 180° around noon.
Specifically we're interested in the solar azimuth at sunrise and sunset - the compass bearing at which the sun crosses the horizon.
It's well known that the times of sunrise and sunset vary each day, thanks to the tilt of the Earth on its axis. This ensures that the Sun is above the horizon for a different length of time each day. But it also means that the Sun's path across the sky intersects with the horizon at a slightly different point each day, hence the gradual shift of where sunrise and sunset appear to take place.
Here's what's going on at the moment.
I've picked Greenwich Observatory as my point of reference, to make the calculations easier. But the azimuth doesn't vary much across London, or indeed across England, even though the time of sunrise may be very different. The azimuth is identical along the same line of latitude.
Azimuth at sunrise, Greenwich, London
See how the sun rises at a slightly different point on each successive day. That point changes by about 0.6° every morning. Yesterday it rose at 90.8°, which is fractionally south of due east. Tomorrow it'll rise at 89.5°, which is fractionally north of due east. Today it rose at 90.2°, which is as near to due east as it'll get. Today is the only day in the first half of the year when the sun rises in the east.
Azimuth at sunset, Greenwich, London
A similar thing happens at sunset. The point on the horizon where the sun sets nudges round each day, and today is the closest day to 270°. Today is the only day in the first half of the year when the sun sets in the west. I must say, I was expecting the key date to be 20th March, because that's the date of the spring equinox, but for obscure geometric reasons the actual date is a couple of days earlier.
Another complication I haven't mentioned yet is height. Greenwich Observatory is 48m above sea level, and I've used that elevation in my calculations. But if it were at sea level then the azimuth would be slightly different, essentially because you couldn't see quite so far towards the horizon. Here's what difference it would make to today's sunrise make if Greenwich Observatory were at a different height.
Azimuth at sunset, 18th March, London
An elevation of 20m would give an angle of precisely 270°, or genuinely due west. I've included 244m in the table because that's the height of the uppermost observation deck on the Shard. If you're watching the sun set from up there then the sun lingers fractionally longer above the horizon, and so sets slightly further north. It's only a tiny difference, but enough to make the Shard's "due west" sunset yesterday rather than today.
And while these changes aren't particularly noticeable over the course of a week, they're considerably more obvious across a year. Here's a table showing the compass bearing of sunrise on the 21st day of each month.
Azimuth at Greenwich on the 21st day of the month
The point at which the Sun rises above the horizon varies by an amazing 80° over the course of a year. At the winter solstice in December it's almost southeast. At the summer solstice in June it's almost northeast. And inbetween those dates it shifts gradually between SE and NE, passing due east in March and September.
Azimuth at Greenwich on the 21st day of the month
Similarly the point at which the Sun sets below the horizon also varies by 80° over the course of a year. At the winter solstice in December it's almost southwest. At the summer solstice in June it's almost northwest. And inbetween those dates it shifts gradually between SW and NW, passing due west in March and September. Specifically today.
And yes, this would all be a lot clearer on a diagram.
My diagram shows the direction of sunrise and sunset in London on the 21st day of each month. You can see clearly just how much it changes, especially in spring and autumn, if less so in summer and winter.
This is why north-facing gardens see hardly any direct sun in the winter. This is why I can almost see sunsets out of my back window at the height of summer, but at no other time of year. This is how Stonehenge could be built so that the sun rises above the Heel Stone on the longest day of the year. And this is why today the sun rises in the east and sets in the west, and will do again in September.
Our ancestors would have known all about shifting sunrises and sunsets, and how they mark the seasons of the year. I wonder how many of us dashing around in our modern technological lives ever realise that this solar ballet is taking place. But smile, because tomorrow the sun rises and sets nearer to the northern horizon than to the south. It may still feel like winter out there, but the good half of the year is on its way.