In ascending order, the cheapest European departure cities with the lowest Emirates economy fares to Melbourne in November are:
Istanbul, Venice, Rome, Birmingham, Gatwick, Newcastle and Heathrow. It’s unlikely, however, that you could save enough to offset the cost of reaching, say, Istanbul assuming that you are UK-based.
In Business Class, the ranked order is Venice, Istanbul, Rome, Athens, Birmingham, Gatwick and Heathrow.
In all cases however, Emirates is not the cheapest on the route – Malaysia has probably the strongest Business fares exIST at present for November travel at £1311 one way.
If you are under 26 then it may be worth checking STA travel, as they often sell cheap one way economy tickets.