Entirely depends on the nature of your visit.
Barbados is not included on the UK Border Agency list for Visa and Transit Nationals and as such you can visit the UK without a visa. If however, you intend to work, study, marry or essentially perform any activity other than short-term tourism then you are likely to require a Visa.
You shouldn't make travel arrangements though without checking first with the relevant authority as visa restrictions and arrangements can change suddenly. The UK Border Agency has a website that will keep you up to date on all Visa requirements.
http://www.ukvisas.gov.UK/en/
Yes, Colombians need a visa to travel to the UK.
Yes, UK citizens need a visa to travel to Dubai.
Yes, Americans need a visa to travel to the UK for tourism or business purposes.
I have UK travel document (blue) do I need a visa to visit canada?
Yes, Australians need a visa to travel to the UK for tourism or short-term visits.
Yes, US citizens need a visa to travel to the UK for tourism or business purposes.
Yes, green card holders need a visa to travel to the UK.
I have UK travel document do I need visa to visit kurdistan?
No
Yes, you need a Visa if you are a Philipino to get into the UK.
No, Israel is of visa free travel for British nationals.
No