As stated, BA and QF have a monopoly of the direct UK-Australia market. Other airlines are of course indirect.

Last time I checked, BA and AY had a monopoly of non-stop flights between the UK and Finland. Last time I checked, BA and IB had a monopoly of flights between LHR and Spain. While I don't check the position on a daily basis, I guess the situation is not wildly different now.

BA and LX will have the monopoly on most UK-Switzerland routes and apparently BA are objecting to SWISS joining OW, yet that doesn't seem to be a problem with the other airlines I mentioned.