GAry 7

The Earth is approximately 25000 miles in circumference at the equator. Thus, a point on the equator revolves around the Earth’s axis at about 1000 mph. At the latitude of London (51 degrees), the circle traced out by London is about 16000 miles, so London revolves at just shy of 700 mph, so the song’s interpretation is probably a reasonable, rounded figure.

That’s orbiting at nineteen miles a second, so it’s reckoned,
A sun that is the source of all our power.

According to here the Earth moves at about 30 km/s in its orbit, or about 19 miles a second.

(skipping a bit)
Our galaxy itself contains a hundred billion stars.
It’s a hundred thousand light years side to side.
It bulges in the middle, sixteen thousand light years thick,
But out by us, it’s just three thousand light years wide.
We’re thirty thousand light years from galactic central point.

Being pressed for time, I’m not going to look those up, but the numbers seem accurate enough for the purposes of the song.

We go ’round every two hundred million years,

According to here the cosmic year is about 230 million years. The song is close enough for government work.

back to the skipped bit…
The sun and you and me and all the stars that we can see
Are moving at a million miles a day
In an outer spiral arm, at forty thousand miles an hour,
Of the galaxy we call the ‘Milky Way’.

Hard to say what it’s referring to here. In our trip around the galaxy, I get a number of around 600k mph, or about 250 km/s. That number seems consistent with some references I found, so I’d say that if that’s what the song is on about, the song is wrong.

According to here the galaxy is zipping through space at around 600 km/s (1.3 million mph). So I will conjecture that the numbers in the song were chosen by onageristic guessing.