Mate as in buddy. We can't all be married to Brian Cox, but we can be his mates. If he'll let us. Which I'm sure he will.
Aaaanyway, that aside (Jeff Forshaw was the other author I was thinking of), the train scenario you've mentioned is a classic relativity idea, but I don't think it's necessary in the explanation of an expanding Universe.
Wherever we look in the sky, stuff is moving away from us - generally speaking all the galaxies we see are getting further and further away (with the exception of a couple, notably Andromeda seeing as it's on a collision course with the Milky Way even at 2 and a half million light years away, but even this scale is pretty small with regards to the Universe as a whole).
The idea to picture it has been shown with balloons or with bread, or chocolate chip muffins and the like. If you imagine yourself as a chocolate chip inside a yet-to-be-baked muffin, you've got some chocolate chips nearby you and some further away from you, in whichever direction you look. As you start to be baked though, the muffin expands and you find yourself getting further and further away from your nearby chocolate chip neighbours. But it's not just you who see's this happening, it's the same for every chocolate chip, every galaxy. If they looked out in any direction, they see every other chocolate chip moving further away from them as well.
The balloon analogy if the muffin didn't help was that if you stick a grid of little bits of blu-tac to the surface of a half-filled balloon, you can see each blob of blu-tac is separated by 2cm for example. When you blow the balloon up further, the space between them expands and you find that it's now 4cm for example, and whichever blob you were on, whichever galaxy you were in, you'd see this same general expansion. In short, it doesn't matter where your starting point is, you'll see the same characteristics of expansion.
So what are those characteristics, how can we tell it's expanding? The one and only Edwin Hubble kicked us off with noting the redshifts of galaxies were increasing, proportional to their distances from us (the further away the faster the apparent movement). As we learned more about certain cosmic events like supernova, we found that some of them can act as markers to gauge distances. X-Ray and gamma ray bursts are similar yard-sticks of sorts.
It's only fairly recently that these things have been used to show an increase in acceleration, let alone an acceleration at all, and of course as more is known more detail can be added to the picture. There are, and have to be, plenty of sources of supporting evidence in order for there to be a consensus, as there is with an expanding universe.
