On 27 January 2017, President Trump signed an Executive Order suspending immigrant and non-immigrant entry to the USA for people from Libya, Iran, Iraq, Somalia, Sudan, Syria and Yemen for a period of 90 days.
If you are a resident in the UK, but are a citizen of one the seven countries listed above you will be unable to travel to the USA whilst this policy is in place unless you have dual UK nationality. However, British dual nationals of one of the seven countries must apply for a visa rather than travel under the Visa Waiver Programme.
The Foreign and Commonwealth Office (FCO) has confirmed with the US government that any British Nationals with dual nationality with one of the seven countries, who is travelling on a British passport from one of the listed countries should expect additional security checks on arrival in the USA.
All UK citizens travelling to the USA need to apply online for an electronic visa known as an ESTA, this should ideally be done at least 72 hours before travel. In certain cases travellers may be required to attend an interview in person to obtain a visa, exceptions from the ESTA programme include people who may have had a criminal conviction, though there are also other categories.
For further information and advice, you should check the Foreign Office website.