I'm a student pilot just about to get my basic PPL and looked into the same thing myself. I can't quickly and easily find the specific part of the ANO right now, but one of the interesting things is that if you fly on behalf of an employer (but not hired as a pilot as such) then the employer can contribute up to ALL of the direct costs associated with the flight.
So, if you work at Joe Blogg's store, you take your boss out for a flight, they could pay all of your direct flight costs. There are very specific limitations (for instance, you must not be in a position where you HAVE to fly) but it could be another way of flying cheaply.
I'll see if I can find the ANO.