The USA has a visa waiver program that means that most British and European citizens do not need a visa to visit the USA. They do need an ESTA though.
The US Visa Waiver Program (VWP) allows citizens of 40 countries to travel to the United States for business or tourism for stays of up to
90 days without a visa.
You can find out more about the Visa Waiver Program at
The ESTA (Electronic System for Travel Authorization) is a fully automated, electronic system for screening passengers before they begin travel to
the United States under the Visa Waiver Program. Eligible citizens from the waiver countries must obtain approval
through ESTA prior to traveling to the United States.
An ESTA costs $21.00 and is valid for 2 years.
You can find out more about ESTA at
Visa Waiver Countries
Below is a list of the Visa Waiver Program countries.
This list is valid at the time of writing.