This might be a bit controversial, but I am not sure people can understand real poverty unless they have lived it, practically and every day. And even then, when you are out of it, it's hard to remember what it was like.
I'm not saying that lovely people can't empathize - they absolutely can - but the empathy tends to run along lines of judgements ('I can see how it would be difficult to afford £20 in one go'). From what I remember, the thing about poverty is that it's the minute-by-minute nature of it that's so wearing. It's the getting up and being freezing cold all day, the having to count every penny, the having to go to lengths in your cooking to eke out ingredients, the devastating panic that sweeps over you when facing an unexpected expense. It's the time it takes to do your laundry at the launderette because you can't in a million years find £150 for a machine - even though you know that it works out more expensive this way in the long run. It's the fact that you pay more, not less, for electricity out of a meter. It's the never having a night out, or a bottle of wine and the social humiliations that go with it. It's the utter, utter self-denial that you have to practice all of the time that is miserable.
I've been there, but am now reasonably off (not rich, not at all rich - but definitely comfortable). I remember it, but it's at a distance from my life now, and that's not the same as being there in the situation. It fades, you forget. But it is nonetheless a whole different experience - my DH has never been properly poor, and while he is very empathetic to others and tries hard to understand, he has never really gone without anything. A while back, we had a period where we weren't able to afford quite as much as usual - I wouldn't say it was a tough time, just a wee bit more constrained - and he was genuinely shocked, surprised and struggling with what I considered really 'easy' bits of self-denial (like not having umpteen holidays a year, not having yet another pair of designer jeans etc). I think a lot of middle class people, when actually faced with a poor lifestyle, would be the same.