Never ever take notice of what Travel Agents tell you when it comes to Visas they are there to sell you a holiday. I can only suggest you contact the US Embassy and ask for their advice. In the current climate failure to declare could possible cause more problems than doing so. There is a waiver system for some convictions. Why not give them a call?

U.S. Embassy London
24 Grosvenor Square
London, W1A 2LQ
United Kingdom
Phone: [44] (0)20 7499-9000

Some information can be found here

https://uk.usembassy.gov/visas

Hello Goddard

This is a tricky one and probably why it is so difficult to get a specific answer which I know you want, especially given the new entry requirements and limitations implemented by the new Trump administration, worth noting is that The Rehabilitation of Offenders Act does not apply to US visa law.

If you haven't already looked at the Official Gov.uk website please do look at that and the official advice https://www.gov.uk/foreign-travel-advice/usa/entry-requirements there are links on there to official websites, use them and be careful not to get tricked in to using money making websites for Visa and ESTA applications.

There is advice on the USA Embassy website and it states clearly

'We do not recommend that travellers who have been arrested, even if the arrest did not result in a criminal conviction, have a criminal record,
certain serious communicable illness, have been refused admission into,
or have been deported from, the United States, or have previously
overstayed under the terms of the Visa Waiver Program, attempt to travel
visa free under the Visa Waiver Program. The Rehabilitation of
Offenders Act does not apply to US visa law and spent
convictions,regardless of when they occurred will have a bearing on a
traveller’s eligibility for admission into the United States.'

So going by that it would be best not to try and enter via an ESTA and Visa Waiver Programme (VWP) but apply for a Visa even although even if issued it doesn't guarantee entry.

Look at this page and check the various link particularly section 4 https://uk.usembassy.gov/visas/visa-waiver-program/

https://uk.usembassy.gov/visas/visa-waiver-program/additional-requirements/

There are contact details at the bottom of the US Embassy webpage so it might be beneficial to contact them.

I hope this gives you some help.

Graham