according to Wikipedia British Guina returned to the (Dutch) Batavian Republic in 1802, but were again captured by British forces a year later and were officially ceded to the United Kingdom in 1814, and consolidated into a single colony in 1831.
The slave trade from Britain had ceased by then - those still in it post 1806 I think could be hung.

Sugar plantations were the mainstay until late 19th C (then Bauxite) - The London-based Booker Group of companies (Booker Brothers, McConnell & Co., Ltd.) dominated the economy of British Guiana as it owned most of the plantations - the British imported Indian and Chinese to act as cheap indentured labourers (about 40 years ago I briefly taught in Georgetown - there had been significant racial clashes post independence.

You need to get which years they are thinking of - if 18th C my guess is confusion with the Guinea coast ( many deaths of slave ship crew but most of the local agents who supplied the slaves were not British but local - the slave ships mostly remained off shore.
If mid 19th C then possibly expats running the plantations whose records might still be held in London or where eever the Brooker archives went to.