Dirk, "Reach for the Sky" is the story of Douglas Bader, based on the book of the same title by Paul Brickhill. It was one of a number of typically British 'patriotic' movies, made in the 1950s, just about the time that Britain could finally start to really recover from the physical and economic effects of WW2 and, in some ways, these were, if not a 'thank you' to the servicemen and women, then at least a reminder, and in many ways an 'eye opener', of what had be done and achieved.
There were quite a few in a similar vein, covering virtually all aspects of the war, mainly in Europe, as it was 'closest to home'.
Others in the 'air war' genre are 'Angels One Five', dealing with the BoB, 'Malta Story', 'The Dam Busters', one mentioned by Wayne, 'The One that Got Away', telling the story of Franz von Werra and quite a few more I can't remember the titles of at the moment.
'633 Squadron' is one of those early 1960s movies which made a big hit and has become a classic, with the title music being another classic 'war themes' hit, and is a fictitious story based on a number of typical events carried out by Mosquitos during WW2. Although by today's standards the use of models in some sequences is rather 'ropey' to say the least, the flying and crash-landing sequences are well done - and oh, if those Mossies were still airworthy today !
One thing you will quickly notice in the 1950s B&W air war movies is the use of whatever Spitfire or Hurricane was available - with low-back MkXVI Spits fighting the BoB, and Hurricanes in a squadron with mixed code letters!