Mapped
London town
Why don't your parents remortgage against the value of their property and lend you a lump sum? Then you pay back the interest to their lender, have a fat deposit to put down and consequently will probably get a better mortgage rate your side too. But your parents will need to trust that you can and will repay their loan, and I don't know what would happen if someone on either side died (always plan for the worst!)
This is what my mum did with my bro, and she is still waiting for any sort of money back He managed to get a mortgage on a low wage by having a large deposit.