Firstly, ESTA is NOT a Visa, it is a waiver and it is vital that you understand the difference. There are specific legal requirements needed to obtain a Visa which an authorized ESTA does not comprise of. If you do have a valid Visa for traveling to the United States then you can use this for the reasons of issue and if this is the case, you do not need to apply for ESTA as well. Do take note that in the same way a valid Visa does not give you a definite entrance into the USA neither does an approved ESTA.
Since 12th January 2009, it has been a requirement by the United States that all British nationals visiting under the VWP (Visa Waiver Program) must apply for ESTA (Electronic System for Travel Authorization). While not being a definitive visa it is a required "travel permit" and applies to anyone entering the USA via air or sea who resides in a country that is part of the Visa Waiver Program. All of those applying through the ESTA system must hold a valid machine-readable passport. A British Citizen without either an approved US visitor's Visa or an approved ESTA travel authorization will not be allowed to board a flight with a USA destination therefore it is recommended by the US Government that you apply for ESTA as early as you can, at least 72 hours before beginning travel to the USA.
If you are a citizen of a country which is part of the Visa Waiver Program then you can visit the USA without a visa however, you do need your ESTA instead. You will find that there are some limitations on the VWP but the most important benefit is that you do not require a Visa. All British citizens holding an up to date British passport can apply for ESTA online which, once approved, will allow you up to 90 days stay in the USA for business, leisure, transit or medical purposes and you do not need to apply for a USA Visa.