Thanks WHBM! I think this journey would have been in Summer 1959. We did stop in Brazil, possibly once, possibly more. We did also have a few hours in Lisbon one time, but that might have been on the ship returning to Montevideo after our summer holiday in UK.
I think BOAC is more likely as Dad was based at the British Embassy in Uruguay (partly trying to help UK trade and industry). The Uk Government preferred British ships and planes to be used. In fact I wonder if perhaps even before scheduled Comet flights were underway there might have been occasional special flights for VIPs/Diplomats/Military etc..