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Does this mean or is there an indirect signals that UK government would be closing borders for all affected countries soon?
No, it means that due to Jamaica's restrictions there may be less planes available to return with.
Their response was lengthy but in essence they said they will try their best to bring everyone home if such case occurs.
This is, for them, a logistic problem. Will the plane needed be there on the 20th for your scheduled return flight?.
Having a reservation relatively soon after the 16th is a positive point for you. Somebody who would be casually traveling from island to island less so.
Assume nobody is interested in keeping peaple stranded. It may not work out exactly as planned, but as seen in the recent past, everybody was able to return.
Keep in close contact with your travel agent and make sure you are available at short notice to leave.
If you are not satisfied with this arraignment, you can make your own. But assume this may be difficult.
Also make sure that your travel insurance covers this situation if you expect them to cover the costs of your private arrangements.