If you are a UK or a US citizen, a passport is the only thing you’ll need to enter Jamaica. Anywhere in the Commonwealth is also fine, with the exception of the Cayman Islands, Sri Lanka, Nigeria and Pakistan. You can find a full listing of countries whose citizens require a visa here.
Should you have any enquiries prior to your visit, there is a branch of the Jamaican High Commission in the UK which is contactable:
Jamaican High Commission
1-2 Prince Consort Road
Tel: +44 (0)207 823 9911