For first rail journey alone, was older than some posters here, younger than others was about thirteen and a half.
This had been for a while, a somewhat vexed matter between me and parental / in-loco-parentis units. Kids at an awkward and obnoxious age can tend to feel that their elders are seeking out all possible ways in which to ill-use their offspring; when in fact parents are usually only trying to follow what they feel is the right course, with an almost impossible task of trying to displease everyone as little as possible. When I was 12 / 13, there was friction between me and my mother (Dad had died a couple of years previously) about solo-rail-travel-or-not, for me. I being a railway enthusiast and familiar with the ins-and-outs of the system, considered myself perfectly capable of managing rail travel on my own. Mum was less sure, and talked theoretically of should the occasion arise putting me on the train in charge of the guard. I found this idea utterly humiliating / infantilising / setting-at-naught of my rail expertise -- not helped by the erroneous picture which I formed, of its involving my having to travel actually, uncomfortably, in the guards compartment along with baggage / crates / bikes / caged animals in transit.
Our worst such bout was in summer 1961, in the course of a holiday staying with relations near Chester. I had my heart set on the idea of -- during this spell -- making as a day-trip, a first-ever visit to the Ffestiniog Railway. Mum had originally seen this as possible, with her kindly driving us to Porthmadog and back, including a return trip on the FR. Various organisational crap happened, in part involving younger siblings, and she had to rescind the driving-there plan. I begged to be allowed to do the day trip by rail, solo (no alternative ways of achieving the objective, were available). I had it all figured out: North Wales Coast main line to Bangor, then to FR territory via Caernarfon and Afonwen, do the FR, and same in reverse it would be simple. Mum took thought, but ended up veto-ing the idea -- no in-charge-of-guard measures considered, even. I, aged just thirteen, was furiously angry; but of course, such stuff happens in life. Some parents tend toward what others see as age-inappropriate over-protectiveness one reckons that individual parents have to do as they feel that they must. In the end, it was another three years before I got to the Ffestiniog.
Family-type situations meant that not a long while thereafter, I spent a couple of years living with an uncle and aunt in Derby. At roughly thirteen and a half, I made my first solo rail journey, between Bishops Stortford where I was at boarding school, and Derby; via London including tube Liverpool Street St. Pancras. With my uncle having made that journey with me at the beginning of that term, he reckoned me with my railways-awareness, savvy enough to do the trip, and others, in future on my own. Had no further solo-travelling issues with any of my olds.