The antagonist and the protagonist have basically the same aim - they both want their old lives back. Or as Islington put it, their 'former glories'. But Richard and Islington take entirely different approaches, and in the end only one of them succeeds.
Richard should have suspected the Angel Islington was up to something. Well, in the book at least. He previously had a nightmare about an figure falling from the heavens with burning wings. And lo and behold, the only character who should have wings doesn't. Hmm, I don't know, maybe they were burnt off?
This isn't shown in the radio version, in which Islington spreads his wings twice, once alone and once for Door and Richard. Judging by their reaction and his comment about being confined, his wings are rather luxurious.
In the book, Iliaster doesn't take the ATM card Richard offers him, even though he's homeless and it's got 15,000 pounds on it. This is because he's also a Belower and he won't be able to get the money out either.