Air Battalion of Royal Engineers, which later turned into the Royal Flying Corps, and if you also consider the Royal Naval Air Service.
A history of the birth of the Royal Air Force, "RAF: The Birth of the World's First Air Force", was published earlier this year, perhaps to profit from that anniversary. It details the genesis of the RAF as an independent service and the reorganization of various air boards and committees into the Air Ministry. The sub-title is misleading. Perhaps a more fitting one would have been: "The Birth of the World's First Independent Air Force". The author is Professor of History at King's College London and presumably knows that Italy's 'Corpo Aeronautico Militare' pioneered military aviation by carrying out both the first aerial bombardment
mission and the first reconnaissance flight, pre-WW1 during the Italo/Turkey War. And France's 'Service Aeronautique', and even Germany's 'Luftstreitkrafte' are a bit older than their Brit counterparts. But I would surmise the editors at the publishing house knew their potential book buyers better and went with the version that would sell.
The author, Richard Overy, is a professor at King's College in London and an award winning historian: Samuel Eliot Morison Prize of the Society for Military History in 2001, plus the Wolfson History Prize and Hessell-Tiltman Prize in 2004. The book is not much over a hundred pages, it is perfect for a quick summer read. And perfect for the average aviation buff. Yet this is not a detailed history.
For someone looking for more beef I would recommend retired RAF Wing Commander Ian Philpott's "The Birth of the Royal Air Force" published by Pen &Sword. Philpott does not have the academic chops of Professor Overy, but IMHO his book has a more extensive scope. Not only a history, it is encyclopedic in its details of operational events, including some first clumsy attempts at CAS, which has generated much interest on this blog in the past. Also gives specifics on early Brit airplane design, RFC airfields and RNAS seaplane bases. A bit spendy, but worth the price. And it was published five years ago, so certainly there are inexpensive used copies available.