I see you are from the UK. You need to talk to a good mortgage broker. Different lenders have different types of loans available. A good mortgage broker may be able to find you a lender willing to give you a stated income loan meaning you don't have to prove income or employment history because you have such a large down payment.
The good news is that you could buy a two-bedroom condo with $400,000. If you can't get regular financing, you could buy a home where the seller carries the loan for you. I have a duplex in Culver City where the seller would carry the loan. It all depends on how much equity the seller has and what their plans are.
I live and work in Culver City. Email me what you are looking for and I will start sending you the latest listings so you can get an idea of what you can get.
Todd Miller - firstname.lastname@example.org