Unless you've bought the most expensive types of tickets, you may not entitled to any refund from Virgin Atlantic.
From their FAQs:
"Q: If a member of my family is taken ill and I no longer wish to travel due to this, am I entitled to a refund?
A: You may be considered for a refund, however, it will depend on the fare rules governing the type of ticket you have as to whether or not you are eligible".
It's not uncommon for the cheapest tickets (on any airline) to have a strict rule of 'No refunds under any circumstances whatever'. The airline will normally refer you instead to your insurer to seek compensation. However I've just entered some random flight dates into Virgin Atlantic's booking system and, upon clicking the link for fare conditions (of the cheapest fare offered for those dates), I found this:
"Cancellations any time ticket is non-refundable. Waived for illness or death of passenger or family member".
So there's a chance that you might be able to get a refund. The only way to find out for sure is to apply:
http://www.virgin-atl...cketrefunds/index.jsp
Chris