British nationals are required to must have an ESTA travel authorization in order to enter the United States by air or sea without a visa for tourism, business, or transit.
U.S. law states that only British citizens with the unrestricted right of permanent abode in England, Scotland, Wales, Northern Ireland, the Channel Islands, and the Isle of Man are eligible for visa waiver and ESTA.
Citizens of the United Kingdom who wish to travel to the USA for other reasons, such as to work or study, must contact a United States embassy or consulate in their country of residence.
For citizens of the United Kingdom who are moving to the United States or seeking permission to work legally in the country, an ESTA travel authorization is not obligatory. Instead, individuals in these situations must apply for a residence visa and/or work visa, in accordance with US visa policy.
Additionally, if an UK traveler wishes to stay in the US for longer than 90 days, they are required to obtain a US visa instead of the ESTA.
If the ESTA is denied for any reason, then you need to contact the U.S. Consulate in the UK to apply for a visa.