This from the gov.uk travel advice
"Temporary immigration measures are in place affecting British nationals who hold dual nationality with Libya, Iran, Iraq, Somalia, Sudan, Syria and Yemen. See Entry Requirements
You’ll need prior authorisation to enter the United States using a British passport, either through a visa, a Permanent Resident Card, or the Visa Waiver Programme. Restrictions apply depending on the type of passport you hold, your nationality, criminal history, and countries you may have recently visited. It’s your responsibility to know and understand the entry rules before you travel. See Entry Requirements."
The only problem is the US embassy has released a statement saying they are not issuing visa form dual nationals and not to apply of turn up for meetings in these circumstances. It's all got a bit Kafkaesque 'you can enter the country with a visa, but we won't give you a visa'