With my household insurance, medical insurance, credit card insurance and the EU's E111 insurance, why should I buy additional travel insurance?

There is a certain amount of cover afforded by those policies but it is not complete. You must ask yourself if the cover given by those policies is as wide as you need. With Credit cards, you are typically just covered for personal accident, e.g. you loose an arm and they pay you £10,000. You are not covered for the medical treatment to cope with your accident or injury.