This is almost certainly going to be unpopular but screw it.
Buying a house is hard but you can do it if you're prepared to sacrifice.
I will caveat this right now by saying that house ownership isn't for everyone. Some folk just genuinely don't earn enough money. If that's the case then you don't want a house, they're really expensive, way more expensive than renting and you'll dig yourself into a hole. That's ok. If you want to change your circumstances good on you; do an OU degree, improve your career prospects or move to a cheaper area whatever it takes ... but if that's not an option you don't want a house it's not worth the financial stress.
OK so if that's not you, if you make a decent wage in a professional job you can do this especially if there's 2 of you.
First thing's first you have to be prepared to budget and cut back hard, if you're not then sorry homeownership ain't for you; like I said before houses are expensive if you can't budget you'll end up losing the house anyway.
So fire up Google sheets right now and write down all your monthly expenses, not just what you think you spend roughly, open up your internet banking and actually put in what you spent the last 3-6-12 months and categorise it: Food, rent, utilities, luxuries, transport, entertainment, charity, then itemise and average it so you know what you spend each month.
Now take a good hard look at that spreadsheet. you need to cut £300-500 a month. Now be honest with yourself do you want to? Do you actually want a house enough to give up your iPhone 6s and buy a cheapo android phone? To sit home with netflix on a friday night instead of boozing up with your mates. To take a packed lunch into the office instead of buying a tesco meal deal. Because these cuts aren't just for now they're for as long as you're paying for this house (or at least until you get a raise and can afford those things again). Nothing should be safe from your cuts. You spend how much on car insurance and fuel? do you actually need a car?
Next get your ass onto moneysupermarket and look up the best savings accounts or save to buy accounts and open one up. Then set up a direct debit for the day after your pay goes in. But not all of your cuts. You need some emergency savings and you'll get punished interest/fees wise if you dip into your new savings account, 75% of what you just cut goes into house savings 25% into a separate easy access savings account (just set it up online with your current bank).
So let's say you managed to cut £500 You save £400 a month that's nearly £5K a year. 2 years of that and you've got £10K with a 95% mortgage you can now afford a house that costs £200K. You've also got £2.5K in easy access savings in case there are extra legal fees or your car breaks down on the same day you move.
This is exactly what my wife and I did before we bought our house. We were fortunate enough that we were able to move in with parents for a year which halved the time it took. That year was a bit crap we didn't have much in the way of disposable income but it was worth it when we got the keys to our new house. The first couple of months in the house were pretty similar money wise too. i.e. we had none. Eventually we both got raises and now we're comfortable again. We did this 2 years ago at the age of 24.