Nope #1 UA & BA are 2 different Alliances UA is Star Alliance while BA is One World
#2 although AA & BA are Both in OW you cant use miles from 1 to fly on the other over the Atlantic
so either youd need to buy some more miles on 1 program , buy a few $$ tkts or spilit everyone up into at least 2 groups
Out of NY UA doesnt fly non-stop, BA flys only to London and even AA doesnt fly to many places. I suggest use BA and the rest on AA that will connect (if London isnt the final destination) on BA so hopefully you all can be on the same flight out of London, but good luck finding 6 tkts on any 1 flight
PS you arent done giving your $$ to BA as they have a fuel surcharge per flight segment = lets say Rome is your final destination then it would be 2 long hauls (to/from the US) and 2 short hauls (to/from London) or 4 segments, then London has the higest departure taxes I know of so it will be anything but cheap. A free AA coach tkt is $125 for taxes alone and thats just non-stop to London
