From a economical side of things:
Do you think those things would go away if budgets were cut to free up the money? All that would happen is for services to degrade. Unfortunatly, we live in a bureaucratic society, and worse for this, a democracy.
Things take a long time to be done, and money disappears pretty easily. For this reason, if the government said it would enforce getting rid of christmas lights, cutting personal allowances etc. little extra money would appear out of it. Our government hasn't much control of where funds go once they're spread around, so it's not just a matter of saying "get rid of this this and this". Plus there's no guarantee that the money put into a 'homes for homeless' scheme would actually get to it. We can't even control funding for big projects like Wembley
It's the same in every country that has this kind of system. I think the only country which is moving in the direction where everyone will be well fed, clothed, housed etc. is China.
Local councils have a bad record for being nice
And as our governments (and people) keep supporting devolution, that's not going to get any better (less control on money). If you do rough adding up, let's say it costs £100k investment for each council house to be built, 100,000 homeless families, that's £10 billion up front to solve the problem, which is assuming that we never have any homeless families afterwards. Realistically, that amount isn't going to be produced overnight without serious degradation of services, to which people will object.
So basically, this isn't solved and won't be (for a long time anyway) purely down to our whole society and system. This applied to every country like ours. Not enough people know, want to know, or care. Does this mean we're not 'developed'? No, if you compare us to 'developing' countries
As for a more personal view rather than a economical view, I'd say that the real problem lies in making sure that people don't become homeless due to something like illness. That was the point of the NHS. The family in that article should have been given extra help for that situation. For people who go homeless because of debt... well that's their fault. They can declare bankruptcy, and if they can't support their children (house, feed etc.) then their children should be taken to a place where they will be. The most important point I think I can make, is that people seem to love giving money to charities to help people abroad. Where is that money for our own people? If all the money given by our people to charity went on our own problems... then I don't think there would be a problem because we have all the funding we need. As well as this, maybe if people looked after their finances better we wouldn't have such a big problem as well. We should look a bit less to our government and more to ourselves to solve this.
That was long.