In order to keep our skies safe, busy airspaces in the UK are divided into 'classes' for Air Traffic management.
Classes A, C, D and E are all Controlled Airspaces- with Class A being the most dangerous airspace.
If your drone weighs 7kg or less, you can fly within Controlled Airspace without getting permission from Air Traffic control. However, its up to you to be fairly sure that the flight can be safely made, and you have to keep 'unaided visual contact' with your drone (those of you who wear glasses are good to keep them on- in fact, we insist!)
If on the other hand, your drone weighs above 7kg and you want to fly in Controlled Airspace, you'll need to get a Non-standard flight (NSF) approval from the relevant Air Traffic control unit. You can find the list of UK aerodromes and their contact details here.
If you're after more information about flying your drone in Controlled Airspaces, visit the CAA's Airspace restriction page.