No, don't bother phoning Titan. They specialise in ready availability - the "Go Now" market. Therefore, they are heavily crewed, with people always on standby within 30 minutes.
Consequently you will almost always be able to bring Titan in if your aircraft goes t!ts up at the last moment. However, it also means that they are incredibly expensive for booking ahead.
Best advice of all is GO TO A BROKER.
Air London, Hunt & Palmer, Air Charter are the three biggest and best, and are all well-established. They'll ensure you won't get stitched up by some unscrupulous operator, and don't charge the charterer commission - it comes off the operator's price.