Sick English among workers in overseas islands (8)

I believe the answer is:

antilles

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'overseas islands' is the definition.
'antilles' can be an answer for 'islands' (I've seen this before). I am unsure of the 'overseas' bit.

'sick english among workers' is the wordplay.
'sick' becomes 'ill' (similar in meaning).
'english' becomes 'e' (abbreviation).
'among' indicates putting letters inside.
'workers' becomes 'ants' (worker ants).
'ill'+'e'='ille'
'ille' placed within 'ants' is 'ANTILLES'.

'in' acts as a link.

Can you help me to learn more?

(Other definitions for antilles that I've seen before include "Organism's complete genetic material" , "West Indian island group" , "Caribbean islands" , "archipelago" .)

I've seen this clue in The Times.

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