The majority of requests may be accepted - but that depends upon what exactly is meant by requests accepted (and I suspect anyway that a lot of people don't actually make the formal application if they are told in advance that it's not likely to be granted)...
When I originally asked for flexible working I proposed to start an hour earlier for 4 days a week, and to work a shorter day from home on the 5th day each week, but offering the flexibility to juggle this slightly within any particular week should the business require it - so no reduction in hours, and no impact on productivity, etc.
What I got offered was "flexible" working which (quote) "would allow me time to get my shopping done during the day" - of split shifts (3 x 2.5 hours/day, with a 2 hour gap between each, and based 5 days a week at an office which was a 5 hour round trip from home on a good day. Oh, and the start time was before the first train of the day could get me there, even if it was on time, and the proposed finish time left me with a 45 minute wait for a train home.
They obviously knew it would be unacceptable, but for the pupose of figures it was considered that they had offered flexible working, so there was no appeal against it, and no chance to reapply for a year.
On a more positive note, after a long battle I eventually managed to get my role moved to a different reporting structure, where work-life balance is actually a consideration, and I do now have the working pattern I was originally asking for, although it's still only a verbal agreement at this stage, not a formally accepted arrangement. Not ideal, but after a while I believe it would be considered part of t's&c's by custom and practice, and I don't think it will be opposed if and when I do make an application to formalise it.