I grew up really poor so I just don't have money management skills
See, I don't see how the two parts of that sentence fit together.
If you're poor, you have to be really careful with your money, to make sure as many essentials as possible are paid, making sure you get the best price for everything you buy, so you might actually be able to cover everything and possibly even have some money left for something non essential. That takes work and good money management skills.
Whereas when you have plenty of money, as you do now (you're both reasonably high earners) then you are able to spend without thinking about it, and can often do this without running out of money. But the problem lies when you aren't achieving your life goals, like buying a house, so you can stop spending £1300 on rent every month. That's over £15k pa that could be used towards paying for your own asset, instead of someone else's (obviously a bit less due to the cost of mortgage interest, but even so).
With £2k pm spare, you could save your £30k in a little over a year, or two while allowing some spending money each month. If you saved £1500 pm for 2 years, that's £36k and would still allow you £250 pm spending money each. That's hardly 'living like a church mouse'. Plus in 2 years time, it might be a good time to be a FTB, if there's a recession, as it might lead to more properties being available, at lower prices.
I'd suggest that you review your budget, and be honest about essentials and luxuries. You might even be able to cut the cost of some regular bills like mobile costs etc, to free up more money to spend and save. You also need to get out of and stop using your overdraft, because the interest charged is very high, so that's even more money thrown away on nothing and is detrimental to your credit history.
Have a look at:
www.moneysavingexpert.com/family/money-help/
But then again, you might want to have a think about whether you're compatible if you have very different attitudes to money, as it's likely to always be a bone of contention between you.