What tool are you using to search? BA's multi city booking isn't very good for highly complex itineries like this. You are best off using Google flights or ITA Matrix.

Also, do you specifically need to go via Miami? BA will try and route you on its flights by default hence the out of the way trip.

I'm not sure what your dates are but have a go with this - it's set to OneWorld flights only and comes in at £887 with two stops, £990 with one. Like Ldnn said it's not the direct LGW flight.

https://www.google.co.uk/flights/#se...017-04-19;tt=m

Alternatively, you could get an ABZ - BGI - ABZ return with the direct flights for £970, you can then get a return to NYC from BGI separately. Another way of doing it as already mentioned.