If you can pay off the debts, save a deposit, and get a mortgage big enough on your salary, of course you can buy as a single parent!
I'd work backwards: a quick look at the price of the type of house you'd like, in the area you'd prefer, then a quick look on a mortgage comparison site, putting in what you think you'll be able to save as a deposit, and see what numbers it comes out with. Then you can adjust what your going to need to save, or the type / area you could get a house in.
I've only ever had mortgages on my own although I bought before having children - it's totally do-able if as pp says you can save the deposit etc. Plus at the moment it's harder to get mortgages. My first property was shared ownership which was brilliant - got a far nicer place than I would otherwise have been able to afford just on my salary. Good luck!
I am a single parent and have just bought a shared ownership property. I really recommend it as i live in an expensive part of London and would never be able to buy a 'whole' property on my own. It allows me to stay in the borough i live and keep my local connections. Have a look at what schemes are available near you.