UK passport holders require some proof of identification such as a passport or national identity card. A visa is not required.
You'll need photo ID to fly, in any case, and a passport is a convenient way of providing this.
Not sure the majority of Gibraltan residents would approve of your answer jenstar. Gibraltar is a dependent territory of the UK, it has it's own constitution and its own elected assembly, but it's residents count as UK nationals for EU purposes
Bit late for an answer but couldnt resist. Yes you need a British passport to enter Gibraltar but not a visa as long as you are from the UK. We do have an airport albeit a small one, but functionable nonetheless, and damn better than others I have been to like Treviso airport (Ryanair fly there to get to venice). Gibraltar is a part of the UK not spain. Finally, Gibraltar residents are not known as "Gibraltans" as is commonly mistaken, but as "Gibraltarians". Hope this clears it.