Most banks will open an account in a major currency, however for travel purposes you're better off with getting an account in a "virtual" bank, such as Revolut. You apply online, receive a card through the mail and then convert your money to USD (orusing interbank rates or directly top-up USD) using interbank rates - either through an existing bank card or via wire transfer. No fees, no charges - unlike what you will usually see with UK banks when attempting to spend your money abroad.
Revolut is technically a British bank, so the answer is yes - it's possible.