If a mortgage lender isn't willing to lend you the amount of money you need – perhaps you don't earn enough, or the lender's not convinced by your affordability – a guarantor mortgage might be an alternative option.
A guarantor is somebody who promises to make your mortgage payments (such as a parent) if you fail to do so. They don't own the property so are not on the title deeds, but they have signed a legal contract with your mortgage lender.
It's possible to get a guarantor mortgage if you're self-employed, though you'll still have to prove your general affordability. In some cases, you might not need a deposit, or just a small one.
A mortgage broker will be able to find you details of the lenders which offer guarantor mortgages and their various criteria.