For some time we've known that drones would start getting a hard time. Regrettably there are those flying these unmanned aircraft that just simply can't be trusted. We've seen time and again drones ending up near airports and posing a real risk to flights.
To counter all that the CAA has released a simple video which clears things up quite well:
What's made clear is that you simply aren't allowed to fly your drone near people or busy areas, you can't use them over mass gatherings like festivals or sports events and you are not permitted to fly over things you don't own.
In reality of course these rules are a little stiff, and as long as you aren't planning to do anything stupid or near lots of people you will be fine. The CAA does suggest that you consider issues of privacy too, which might lead you into trouble with different laws.
Also, if you're flying for commercial purposes - to make money - then you must seek permission from the CAA via its website first.