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.
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Under Visa Waiver Program (VWP), the system established by U.S. government, those approved for Travel Authorization through ESTA are permitted to travel to Hawaii without holding visa. Although visa is not required for general trip to Hawaii, be sure to apply for ESTA before travel.
If you have a British passportyou don't need a specific US Visa for UK citizens to enter the US, you only need an ESTA. The ESTA permits qualifying nationalities to enter the US for tourism or business motives. Any traveler that's eligible for the ESTA can enter the US by air or sea.
Domestic travelIf you are flying to Hawai'i within the United States, you only need a valid government photo ID. A list of accepted forms of ID can be found on the TSA website.
New York visa and entry requirementsIf you're a citizen of a country covered by the Visa Waiver Programme (such as the UK), you will need to have a valid e-Passport along with an approved ESTA to enter the USA. You can identify an e-Passport by the 'chip' symbol on the front cover.