These NAS-GCM reward flights seems to be bookable under an RFS pricing model so one way in Y is 4000 avios and £17.50 fee. This is what is quoted and books as on ba.com. I don't know of any examples where you book a reward ticket for a specific price but are asked to pay extra taxes/fees/charges at the airport later.
If I look at a revenue ticket the total taxes/fees/charges are £121.10. However, you are only required yo pay the RFS fee which is a cap.
C9AD $6.60
Security Fee - Bahamas $7.00
PODO $10.00
Airport Facility Fee - Bahamas $38.00
Passenger Departure Tax - Bahamas $29.00
Carrier imposed charge $30.50
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Total charges $121.10