I know plenty of people who live in benders, tents & the like with or without babies, I don't think its that remarkable & can't see why on earth SS would have any interest in them.
I suspect that their story has been mangled out of all recognition by the Guardian the way these things always are, you'll probably find that the bloke is working & that's how they plan to save up for some land while the woman does the chores or vv. And I bet any money that the 'getting up every 2 hours to put wood on the burner' actually translates as :
journalist - don't you freeze overnight
woman - meh, if its really cold we chuck a bit more wood on the burner when baby wakes up for a feed, at the moment she's up every 2 hours anyway . . .
or something to that effect.
And while you can't just buy a bit of land then build an eco-home there are ways round these things (a few councils even have specific sustainable housing policies these days).