The railwayy can't fine you. A fine can only be issued by a court following a prosecution.
Your best case if you get caught is you get issued with a penalty fare (£100) and are required to buy a new full-price ticket. That's assuming you're in a penalty-fare area and the person who checks is authorised to issue penalty fares.
Your worst case scenario is that you get reported for prosecution, and then get prosecuted. I believe the fine is up to £1000, and comes with a criminal record.
The railway company might also choose to check whether you've been buying child tickets previously; and if so, why.
If you were genuinely 15 but looked like you might be older, then you'd need to carry proof of age -- you can get a "Child Rate Photocard" for rail purpose for free; see
https://www.nationalrail.co.uk/on-the-train/train-travel-with-children/ ("We suggest that children who look older than 16 carry a form of ID to show that they are entitled to a child rate fare. For example, a Child Rate Photocard, which can be obtained for free at any staffed National Rail station") Obviously that doesn't apply to you.
I would submit that if you're travelling on the railway using a concessionary fare, then you should expect to be able to provide evidence that you're entitled to that concessionary fare.
Your travel plans indicate that you'd need to change trains at least once in each direction, so you could have your ticket checked at least four times. Do you really want to take that risk?
You're eligible for a 16-25 railcard which would provide a one-third discount on this ticket, at the cost of £30 for a one-year railcard. The discount even on this one trip would pay for the cost of the railcard.
Disclaimer: I'm not a lawyer, or legally trained.