Keep in mind that from the U.S. government perspective, your UK citizenship is irrelevant in this circumstance and that you will be violating U.S. law by spending money on the island, or using Cuban owned transportation to get there. What jbcarioca is suggesting is the way to avoid getting caught violating the law.
*Note: This is not an endorsement of the law, merely a restating of the law as I understand it. Also, please recognize that I am not a lawyer, and this should not be construed as legal advice.