it has to be fairly close to the maximum range of a B772,
It's getting there but you've still usually got a little wriggle room, and there may be the option to trade payload for fuel if the bad weather is forecast and you know you may need the gas ( the only "close" in alternate for a 777 would be Montevideo - which shares EZE's weather. Failing that you're looking at alternates a significant distance away).
Whatever the alternate when making the fuel decision in London you're working on a forecast that will be well over 12 hours old by the time you get to EZE, and there's also the problem of the quality of the forecast.....and that's a problem not just confined to EZE.