Because I live mainly in Israel the iTunes store doesn't want to accept payment using a Visa debit card linked to a UK bank account. Why shouldn't it? And what can I do about it?

As far as I know debit cards are no longer accepted as a valid payment method by iTunes - they are not listed on this page and there have been a number of posts about them being declined. Do you have a credit card ? To be able to use a credit card on your Israeli account it will need to have been issued by a Israeli bank (you can't use a card issued by a bank in another country).