The tabletop RPG isn't a good guide. They have changed things to better suit the different play.
Why doesn't everybody own a spaceship?
There are two possible reasons that I can see. Either the life of a commander is so cheap that loitering is a capital offense, or the ship/training is too expensive.
It seems to me that to single out pilots for extreme death would be unreasonable. Everybody's life is cheap in the Elite universe. The Pilot's Federation would not have a monopoly on training; that would be against the free market ethic that is at the heart of the Elite universe.
So the ship is too expensive for most people to afford.
Stealthie's estimate of $128M might be the price of a top of the line military fighter in today's world. All things being equal then that is what it might cost to build a Sidewinder today if the technology was there. But this isn't cutting-edge technology by the time of ED and the Sidewinder is the lowest of the low.
Private airplanes cost from $30,000 (Piper Cub) to a few million (a Learjet is $5M). A military jet trainer is $20M.
Ian Doncaster's suggestion of $64,000 is around the same as a high-status car. A Tesla model 3 will set you back $35,000. No ordinary person could afford one and many people who could stretch to it have better uses for their money. The Pilot's Federation doesn't give them out; we are loaned one by an anonymous benefactor. If we assume that the benefactor is loaning out a lot of them (unlike the original game, we are not unique) then it's unlikely to cost many millions. Not many people
need the Sidewinder for more than a month or two, although the game doesn't insist they are returned. But there are a lot of players. $64k seems about the least amount that such a person could invest in such a project and while I can just see it reaching Learjet levels, I think $20M might be unrealistic.
Perhaps if we think of FSD-equipped ships as jets, then intra-system ships might be $30,000 upwards with inter-stellar ships starting at $500,000 (matching the Eclipse 550 -- advertised as the cheapest twin-engined jet.)
The question is, can a middle-class citizen dream of owning a Sidewinder? If it's $64k then they can. If it's half a million or more then they can't. What sort of universe is ED? What do you want it to be?
So to answer the OP, £128M seems about right.
In Elite Dangerous times, I think $64,000 is the right ballpark but it would be reasonable for it to be anything up to $5M.