How about "伦敦O2室内运动场" Though O2 is still odd to the Chinese language itself...It is afterall not pure Chinese.

I would call it 伦敦O2大剧院.

I think here O2 Arena can translated into "O2娱乐中心" better than “竞技场”. It contains various buildings related to concert, entertainment, and exhibition ,etc.

体育场 a stadium, an outdoor arena with platforms for watching, like the Bird's Nest [a big one] 体育馆 an indoor sports arena, usually with more than one floor, where people do indoor sports 竞技场 usually for computer games or other games, but "il Colosseo" in Rome is also called 罗马竞技场， in other cases, we seldom use it 运动场=赛场 usually used to refer to an occasion where it is not necessary to point out in what kind of building that you do sport eg. 一些运动员在运动场(赛场)上接受记者采访 But actually, you know, Sport hasn't been seen as an very very very important aspect that can express a country's spirit [ I mean for all the people, not only the national players ], so sometimes we don't tell the difference between an outdoor and an indoor arena ( and there are very few stadiums in China I think). Maybe that's why someone has told you “体育场” :)