why doesn't your partner move out of his arranged overdraft and into your house, houses are more comfortable than overdrafts.
but seriously. I think if it's an arranged overdraft of reasonable size and not getting bigger and bigger it probably won't affect your credit rating and thus your ability to get a mortgage. but he is paying interest on this and so should be trying to get back into the black as soon as possible.
declare it as a debt in your mortgage application, along with credit cards, loans, etc, as you will be legally obliged to do. if it does limit the amount to be borrowed it may help you to avoid overstretching yourself, at least.