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I think you're probably wise to look at Z class fares on LATAM, though the cheapest from London may require going via Brazil and/or MAD. A search on LATAM Z fares will show some experiences there. I can see some fares below £1600. On BA direct you're looking at £2300, maybe saving a hundred or two if starting via DUB. I would keep an eye on prices from Italy and hinterland since Alitalia have a low price from Rome at the moment, which competing airlines may want to match.