|See this and weep, Mr Mayo|
First, I worked at BA for 17 years and met quite a lot of pilots, and many of them were jolly nice people. But almost all were great spinners of yarns. I wouldn't believe a word they said. More to the point, though, as presented, the question bears a considerable resemblance to that hoary old favourite 'How long is a piece of string?', because the proper answer is 'It depends what you are looking at.'*
The furthest anyone can see dwarves the 250 miles answer to a ridiculous extent, but let's work up to it. The human eye is actually very good at detecting photons - it only takes a few to trigger it. This means that on a clear, dark night you can see a candle flame around 10 miles** away, which is pretty impressive in itself.
But a candle isn't exactly hard to beat. Anyone seen the Moon? Yup. So have I. That's around 230,000 miles away. Makes 250 miles seem a little weeny doesn't it? And we haven't started. The Sun is further still, and stars take us out even further. But let's push it to the limit.
The generally agreed 'furthest thing away you can see' (subject to some superbright thing flaring up in the future) is the Andromeda galaxy. Want to find it? One of the most recognizable constellations is Cassiopeia. The five main stars of the constellation form a large letter W, which is hard to miss (though you may see it looking more like an M). But it’s not Cassiopeia itself we are interested in.
If you think of Cassiopeia as a W, treat the second V in the W as an arrow and follow its pointer by a distance that is about the same as the entire span of Cassiopeia. This will have taken you into the much less obvious constellation called Andromeda. And around the point you arrived, a little fuzzy patch of light is just visible with the naked eye.
That fuzzy smear is the Andromeda galaxy, the nearest large galaxy to our own Milky Way. But ‘near’ is a relative thing in intergalactic terms. The Andromeda galaxy is 2.5 million light years away. Let's do a bit of approximate maths to turn that into more familiar units. A light year is the distance light travels in a year. It goes around 186,000 miles a second, so that makes a light year around 186,000 x 3600 x 24 x 365.25 miles. Call it 5,869,713,600,000 miles. So the Andromeda galaxy is around 14,674,284,000,000,000,000 miles away. So the figure given on Simon Mayo's show was around 58,697,136,000,000,000 times too small.
Even by broadcasting standards, that's a pretty magnificent level of inaccuracy.
* This assumes, by the way, that we are talking about seeing with the naked eye, and someone who has good eyesight.
** For easy comparison with the 250 miles, I am abandoning my usual metric units, so those who don't use miles will have to grit their teeth and mentally multiply by 1.609 to get kilometres.
Image from Wikipedia