If your sole interest is video...
DSLR cameras are largely optimized for still photographs, with video largely as an afterthought. DSLRs can take quite decent quality videos, but it is not their purpose and they have drawbacks, two among which are the relatively small size of their sensors and their overall shape and configuration that is less amenable to being held steady for longer periods of time without the need to mount on a tripod.
For a thousand pounds sterling, which today converts to about $1,520, you can get a top-of-the-line consumer DV camera (and a lot of change back from the vendor) or an entry-level professional DV camera like the Sony HVR-HD1000U ($1,525 at Full Compass) or Canon XA10 ($1,309 at Ryther Camera). The lenses and features are optimized for video, the sensor is much larger, their autofocusing is better suited to continuously track moving subjects, their ability to transition between lighter to darker fields is superior, the built-in mic is much higher quality, and you get such features as slow-motion and night vision in many models.
They can also take still shots, but they are optimized for video. Since your primary purpose is video, I would suggest that a DV camera is what would come closer to giving you the results you desire.