Can I travel to the USA with a criminal record?

The USA have a visa waiver scheme for anyone holding passports from certain countries (British passports are included) as long as that person has never been arrested.

As you have a criminal conviction you’ll need to apply for a visa, and possibly a special restricted visa. Applying for a visa will require you to schedule an appointment with a US consular officer at the US Embassy. Bear in mind that the process of applying for a visa can take a long time and should be started as early as possible before travelling.

If you attempted to travel without a visa US immigration would be within their rights to deny you access to the US and if this happened it would become very difficult to enter the US at any point in the future.