I am guessing from your mention of moral turpitude that you are referring to a US visa.
Are you thinking about a US visa because you are going to be spending more than 90 days there, or because you don't think you will be allowed in on an ESTA? My answer below is based on the assumption that you are just wanting to visit the US as a tourist or for a short business trip under 90 days.
Firstly, the term "moral turpitude" has now been removed from the ESTA form. It now asks a vaguer question about whether you have been arrested/convicted for "a crime that resulted in serious damage to property, or serious harm to another person or government authority". It is up to you whether you think you can say no truthfully.
Have you been to the US before? Either with a visa or on an ESTA? If you have been before and disclosed your conviction then you will need a visa, but if you haven't been before they have no way of knowing about it.
The US has no access to the UK Police National Computer (PNC). The only way they can access your information is by an individual, real-time request on a case-by-case basis, and they require reasonable suspicion to be able to ask the UK for this information. They cannot ask the UK for your information simply as part of a random check. I.e. if you have never been to the US, or if you have been there before on an ESTA and ticked "no" to all the questions, you will be absolutely fine.
Seriously, just use an ESTA and tick "no" to the question about criminal convictions.
Look online and you will find hundreds of anecdotes from people with very serious criminal records who have ticked "no" on an ESTA and got in no problem.
They are not interested in people who copied coins 40 years ago - they are interested in terrorists, drug dealers and paedophiles.
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If you actually do have to apply to a visa (if you're moving there or staying more than 90 days in a year), then of course you will have to disclose your conviction in the visa application as you will most likely need to produce a police certificate. You will have to make an appointment at a US embassy and have an interview with them, where the conviction will come up. Seriously, your conviction is so left-field and old that I can't see them caring much about it. Anyone who has a violent, sexual or drug conviction need not bother applying for a visa as it will be arbitrarily rejected, but this conviction is so odd that they might not even have heard of it. Also, the fact that is't been 40 years since the conviction and you (presumably?) haven't had any brushes with the law since, are a big advantage for you.