Just because you don't understand how something is possible, doesn't mean it's impossible ;).
I'm single, I have no Children. My share of rent is 400/m, chuck on ~100 for utilities. I live with 3 others. It's north west London, around a half hour - 40 minute commute by train into central. I leave the house every day. I wouldn't agree that it's "barely a step above poverty" as I grew up in poverty and I've probably never been happier, or healthier.
As for watching every penny, yes and no. Usually I spend around 20-30/week on food. Which is more than a friend who is actively trying to watch his spending and minimise his outgoings. What I don't do, any more, is eat out or drink the likes of Costa. I stopped drinking costa once I tracked my spending on it for a couple weeks last year and saw in front of my eyes I was spending ~10/day on, quite frankly shitty coffee.
The eating out part started off last year purely for health reasons, I wanted to trim down some weight, cut down on my processed food and sugar intake. Subjective of course, but I think you would be amazed at just how bad things taste once you've eaten "clean" for a few weeks. For instance last week I popped in to Wenzels and grabbed a sausage roll, took 1 bite at it looked down and thought what the hell is that, that isn't meat. I chucked it in the bin outside the door and grabbed a packet of peanuts. I used to enjoy the occasional pasty but I think my taste has changed.
Food wise, I eat a nice bit of steak once or twice a week, chicken, fish, fresh vegetables and a range of nuts. I spend ~ 120/month on supplements and protein powder. It can be done, just shop smartly and take advantage of bulk buying in combination with offers and you automatically save a fortune. I don't do the whole cook 14 meals on a Sunday thing like another 1 of my cousins but that's because I've tried it and by Thursday I think the food loses its taste.
Just remember little things add up while your on the go, so those 2 coffees, a snack here, bit of lunch there and you've easily spent 15 in a day, multiply that over the course of a year and you've sunk ~4k on crap with little nutritional value, just to keep you going. A travel mug for your own coffee and making your own lunch will save you money in the long run and it doesn't have to be time intensive.
Your best tool for reducing your out goings is a bit of paper and a pin. Sit down for an hour and work out what your spending and where you can save money.