Low deposit will i get accepted?

Hi,

I would like to buy my first house towards the end of next year. I earn £40k a year and i want to buy a flat in south london for around £180k. I have £10k at the moment deposit wise plus i am going to sell my sports car. So i am hoping to have around £25k to cover deposit fees etc. I have a good credit rating. I was turned down for a loan from my bank earlier on this year, they asked me to pay off my overdraft first. I did that and was accepted 2 months later. The loan will be paid off before I apply.
Do you think £25k will be enough and what do you think my chances of being accepted are? I have no credit card debt or overdraft. I am concerned as i keep hearing stories about people being turned down with much larger deposits than me and earning more. Is there anything i can do to increase my chances of getting accepted next year?

Thanks in advance.