On the credit score thing: you need to be out of your overdrafts consistently. That should be your first 'savings' goal. You say you don't have money to spare for credit cards - proper use of credit cards shouldn't cost you anything and will raise your credit score. You should be able to get a credit card with a low limit (and probably a relatively high rate) quite easily from your bank - set up a Direct Debit to pay it off in full every month and simply do some of your regular spending from that card rather than with your debit card or cash.
On the savings thing: You'll probably need to prioritise the house over all other savings goals, probably including your wedding, I'm afraid. Remember that once you're in a house you own, the money spent on the mortgage becomes, in a sense, the house savings, allowing you to save for other things.
It may also be necessary to revise downwards your homebuying goals. If you've been looking at prices for 2 bed houses, try looking at 1 and 2 bed flats. It gets you on the ladder, and especially if you're in the same area you want to stay in, a rising tide should lift all prices relatively proportionately. How I think of it is "A 1 bed flat is always going to be worth a 1 bed flat, no matter what happens to the prices"