Sorry, Daffy, that's not wholly true.
While a conviction for an offence of 'moral turpitude' normally creates an automatic bar to admission into the USA, Section 1182 (2) (a) (ii) of the US Immigration and Nationality Act provides an exemption for anyone who only committed a single offence of moral turpitude, while still a minor, provided that the offence took place more than 5 years before the application for a visa. (If the minor was sentenced to any form of custody, the 5 year period would commence from their release from such custody).
So, Steeley, if you have no other convictions (or any other form of criminal record, such as a caution or reprimand), you're not automatically banned from entering the USA. (However, even a simple reprimand for nicking a Mars bar would be enough to count as a second offence of 'moral turpitude').
You're not eligible to travel to the USA under the Visa Waiver Program (with an ESTA), so you'll have to go through the tedious process of applying for a visa. That involves obtaining a copy of your police record', from your local police force, and booking & attending an interview at the US Embassy in London. You should allow several months for the whole process. (The police have up to 40 days to respond to your request but they've actually been known to take longer. Then there are other delays as well).
Since you're not automatically barred from entering the USA, your visa application might not have to be referred to Washington. (That's automatic when someone is barred, as their visa application is treated as an application for a 'waiver of inadmissibility'). However it could still occur. If so, the shortest total processing period would be around 5 months. (I've seen a wait of 15 months reported here on AB).
Since your conviction was as a minor, you might well get a visa, but it would still be extremely unwise to book any travel until such time as you had.