You already know the world has a food waste problem. Jamie Oliver has made a big enough fuss of it, along with every Masterchef contestant who proudly makes a point of cooking tripe. And for good reason: around a third of food produced globally is never eaten, meaning if food waste were a country it would be the world's third largest emitter of greenhouse gases, behind the US and China.

This isn't just an environmental issue, either: despite our massive surplus of food, an estimated 8.4 million people in the UK alone struggle to get enough to eat.

The problem is obvious; what's less clear is how we solve it. Like a lot of people, I've always been squeamish about out-of-date food and leftovers. I'd struggle to get on board with that tomato-tinged container you microwave every afternoon in the office kitchen, even though – ultimately, despite how violently it makes me retch – I know it's what I really should be doing.

Project Drawdown's list of 100 solutions to tackle climate change found that cutting food waste is the third most immediate and impactful thing we can do to help battle global warming, behind using wind turbines and better managing refrigerants, and ahead of switching to a plant-rich diet.

So: it's about time I cut my bad habits – no more throwing stuff out the day it hits its best before date, or chucking a perfectly good plate of surplus food. For the next week I'm going to live entirely off meals that are past their best, destined for landfill or handed out for free for whatever other reason that might be.

In recent years, a number of apps have cropped up aiming to tackle food waste, including Olio, which offers free listings of unwanted food from both companies and individuals, and Too Good to Go, which offers surplus food from shops and restaurants at reduced prices.

"Throwing food away is one of the world’s dumbest problems," Jamie Crummie, Too Good to Go's cofounder, tells me. "In the UK, we're throwing away 10 million tons of food each year, so it's a huge issue."

I start my week off by checking Olio, hoping to bag some free stuff. While a ginger beer plant and some bottles of mustard are tempting, neither will provide the sustenance I need to see me through the next few days. So I try Too Good to Go instead.

I get a cheap breakfast from veggie restaurant Tibits near Waterloo. The portion is massive for £3 – beans, egg, potato and some dry discs of bread, which are less good, but still edible. Next, I head to the cafe in Tate Modern to eat while I check the apps for more food, but there's still not much about on Olio except for some half empty bottles of condiments.

Starting this week, I thought I'd be spending the week strolling around the leafier parts of London, picking up unwanted sourdough from middle class mums, but it's not as straightforward as I'd planned. Despite checking Olio every few minutes I don't find anything worth taking for free for the rest of the day, so when I get hungry again I spend £2.50 on a couple of leftover slices of pizza from Voodoo Rays. You can get alright frozen pizzas for around a quid in most supermarkets, so it doesn’t exactly feel like a great deal. The slices are cold, but they're enough to tide me over – and they would have ended up in a skip if I didn't rescue them.

The next day I finally make headway in my search for free stuff. A woman called Eve is offering an out-of-date curry ready meal on Olio. Earlier in the day I also scored some free pita bread, which works well as a makeshift naan. I add some spring onions and coriander from my fridge, deciding there's no point saving other people's food if I waste my own. Once I get over my fear of food poisoning it's a decent meal, and the first properly hot food I eat for a couple of days.

Zoe Morrison, sustainability blogger and author of Eco Thrifty Living, says she used Olio when it first came out a few years ago, and managed to grab about a year's worth of crackers, pesto and other bits that were left over from a food festival. Before using the app, she also tried to set up her own food waste group on Facebook, which was met with limited success.

"I found that people didn't feel that comfortable taking food from strangers, especially if it was part used," she says. "They were happier to take food from people they knew."

I get a similar reaction from friends when I tell them what I'm doing, but it's not like I'm taking food from stranger's plates – everything so far has been sealed. Zoe says that although her food waste group never really took off, her friends now share in a more informal way. "Setting up the group raised the point about food sharing," she says. "Once I'd done that, we didn't need the group, because they would just message me, or I would message them asking if they wanted something."

As well as used bottles of sauce, Olio is mostly full of listings for surplus from bakeries and London's 240-odd Pret a Mangers. This city absolutely loves overpriced sandwiches, and I'm more than happy to capitalise on that by taking the leftover ones Pret has deemed unsellable. For a few days this is alright – who doesn't want to eat a cheese baguette and plate of pastries for dinner? But after a while I start feeling the need for some proper food.

Although it's mostly full of restaurants and caterers, Too Good to Go has some listings for groceries. The only big British supermarket on the app is Morrisons, and each store only has a few £3 "magic bags", which consist of around £10 worth of fruit, veg and baked goods, on offer each day. I fail to get one the first couple of times I try, but Jamie lets me in on a secret: the listings go live at 6:15PM every day. I refresh the app bang on that time and manage to reserve a bag of unwanted and out-of-date groceries.

The box consists of a bag of potatoes, sprouts, parsnips, peppers, cress, a stale baguette, 12 chocolate brioche and some flapjack bites that are all past their best but still edible. It's enough food to see me through the last days of the week if I just boil the veg into a big stew.

So my zero waste week is fairly successful – London is full of surplus and unwanted food, if you have time on your hands to find it and you're not too fussy about what you take. I spent £10 on food over the week and another £1.50 on a bus fare to pick up some pastries on a day when I got fairly desperate for something to eat.

That said, being in London, and having all that time on my hands, put me at a considerable advantage. Changing my home postcode on each app to random spots across the UK, there was a huge variety in the both the number of users near me and the availability of food. So can locally-focused food waste apps really make that much of an impact on such a massive global issue?

Food sustainability activist Josephine Liang thinks so. A couple of years ago she spent three months eating only food that was destined for landfill, using a combination of food waste apps and dumpster diving behind supermarkets, which she says opened her eyes to the scale of waste: "You get all sorts – sometimes they just throw out excess stock, rows of biscuits that aren't even out of date."

Josephine says food waste is still largely invisible, despite getting more attention in recent years. A lot of food is squandered before it even gets close to consumers – with fruit and veg often discarded further down the chain because of requirements about quality and appearance.