British Nationals do not require a visa to visit Barbados. You will be granted a specified period of stay on arrival, which allows a maximum stay of 6 months. If you wish to stay longer, you must apply and pay for an extension through the Barbados Immigration Department.
Your passport must be valid for the intended duration of stay. You will be required to pay a departure tax, which is normally included in the cost of your flight. You should check with your airline to confirm this.