My 14 year old Son has won prize money in the EPIC fornite competition - Tax on his winnings?

Anyone help as to whether that was the right thing to do?

I can't write as to whether or not using your UTR was the right thing to do or not as I am unfamiliar with both US and UK tax laws and procedure.

Are they allowed to do that...?

Yes, they are allowed to do that under withholding tax laws. This IRS publication writes about withholding tax starting in page 3. Essentially, it's the responsibility of the company that is paying your son the prize money to withhold some of the money (in this case, 30%) as taxes.

One of the reasons for withholding tax is to ensure that foreigners who made money from activities in the US pay taxes. As it would be highly inadvisable to pass that responsibility to the payee (due to ease of tax evasion since you aren't in the US), it is usual for countries to hold the payer responsible instead, hence the reduction of 30% prize money.

...and if so how do we get the 30% tax back?

As to getting the tax back, this is usually known as tax relief. This UK Government site has some information on it. As I've mentioned, I am unfamiliar with UK tax laws. Theoretically, you should be able to claim it back as you aren't supposed to be taxed twice on the same income. Practically, however, I would advise giving a call to IRB directly, explaining the situation, and getting a direct answer on this issue.

Do remember that this isn't a clear cut case, due to the actual payee being your son and not yourself. Also, online game winnings are a bit difficult to pin down right now, as far as I can see from Internet research. Most searches jumps straight to gambling winnings, but I would personally link Fortnite to sports/competition winnings. But, and I can't say this enough, I am, in no way, familiar with US and UK tax laws and you should definitely find someone who is to give proper professional advice.