Writing from an American perspective, I found this book an excellent volume about The Proms, although it's not completely a straightforward history from the beginning of the series, in 1895, through the mid-2000's. It's also a somewhat idiosyncratic compendium of chapters from several different authors, fairly linear in history through the Robert Ponsonby era (up to 1986), but then branching out after that with chapters about several different Last Nights over the years, and a chapter devoted to the Promenaders ("Prommers") themselves, the standing-room audiences.
Because The Proms are such a very British institution, the specific cultural references and personages in the early years, in particular, will be somewhat lost on US audiences. The pictures and images from early popular publications (e.g. Punch) are very enjoyable as well, helping to bring the prose to life.