Let's say that you're a 50% shareholder in a flying club which is a limited company owning and operating several light aeroplanes used for the flying instruction and recreational flying of its members. Technically these aircraft are the property of the shareholders and hence you 'own' 50% of them yourself. The Revenue will certainly take an interest if you take advantage of this situation by, for example, flying 'your' aircraft at advantageous or unreasonable hire rates exclusive to yourself. But if you pay the same rates as the members of your club, you will not be receiving any benefit in kind.
If I use one of my light aeroplanes to fly somewhere and back in a day and hence am able to do more work at the place I fly to than I would had I driven there, it would be my employer, not me, who would be benefiting. I can claim the equivalent road distance (most direct air navigation route including any allowance for prohibited airspace) at an approved mileage rate so long as I have prior approval. I know of several people who have done this - there are stipulations and it does require honesty. For example, I cannot conduct any training on such a flight - so when I flew from one aerodrome to another for a meeting a few years ago, I had approval to claim the mileage. (50 min by Cherokee or 2 1/2 hours by road!). However, there was a chap at my club who needed to fly the peculiar PPL renewal that was then in force for some pilots which required a landaway navex and return to an aerodrome more than 50 nm away - and this fitted the bill perfectly. So he paid the going club rate, he flew it there and back under examination conditions - and I didn't submit a claim. No doubt had I done so no-one would ever have been the wiser - but that would have been fraudulent.
Noggin is right about those charitable folk who enjoy horse racing so much that they are happy to fly jockeys around for free......!!
Never do anything which could be construed as being 'illegal public transport' - just recover 'reasonable' costs for your travelling needs in an honest manner.