If my insurance is refused due to my pre-existing medical condition, can I still take out travel insurance with Direct Travel Insurance?

Yes, but you will not be covered for any complications stemming from your uncovered pre-existing medical conditions or from any condition which is medically related to your uncovered pre-existing medical condition(s). You are able to purchase a policy immediately online with no cover for your pre-existing medical conditions, you should still go through the medical screening questions and medical warranty in the booking path answering all questions fully.