Looks like trains would take a few days. Have to use a major air carrier to get there? Or is there smaller airline that is good for the job?
Larry Check skyscanner.com for discount airlines. Also note what airports you fly in and out of. If they are much farther out of the city, may not be worth it. Just read the fine print because they are extremely strict about luggage weight and size. Penalties can be more than the rest of the flight! Price starts out small but goes way up! Also charges for seat assignment or first boarding, using your credit card, etc. But they can be a great bargain. You need to know the details to make sure it works for you! Bobbie
airberlin has flights from vienna to both London Gatwick and Stansted.
"Days" is a bit of an exaggeration. See http://seat61.com/Austria.htm for the best way to do it by train.
Think about expanding your trip. Vienna to Frankfurt 7 hours by train Frankfurt to Paris 4 hours or to Brussels 3 hours Paris to London 2.3 hours or from Brussels 2 hours Frankly I'd rather go through Paris, if I had the time to stop for few days. Frankfurt is a great place to spend 2-3 days too.