Upvote:2
The following is copied from the Canadian Government website.
"To apply for a work permit at this visa office, you must be legally admitted to or a citizen of a country that is served by this visa - office.http://www.cic.gc.ca/English/information/offices/apply-where.asp "
Barbados and UK are both on that list. So in other words, according to the Government of Canada, you are allowed to apply, just by being a citizen.
Here is a link to the website which has more information and a contact phone number to call for more information about this.
http://www.canadainternational.gc.ca/united_kingdom-royaume_uni/visas/work_temp_travailler.aspx