You can fly directly too and from Gibraltar via British Airways and Monarch Airlines.
Both airlines offer several flights a day from various airports, all within the UK, including:
British Airways: London Heathrow, London Gatwick
Monarch Airlines: London Luton and Manchester Airport.
For more information on flight schedules, pricing and booking, please visit the airlines websites:
British Airways: http://www.ba.com
Monarch Airlines: http://www.flymonarch.com
Alternatively, you can travel to Malaga Airport on the south coast of Spain and travel down by bus or car.