I don't think that George Bush and Gordon Brown were referring to the thinly veiled (or often unveiled) anti-semtiic trope of the New World Order conspiracy theory which is basically an updated version of the protocols of the elders of zion (the ultimate conspiracy theory).
But the thing is (as I expanded in my later post), we don't know what they were referring to; just as we don't categorically know what anybody referring to the NWO believes in. Many of them are anti-Semites, but many of them are not.
I think it's far too easy to take a wide general term, attach a single one-size-fits-all understanding to it and then, based on that strict definition, condemn everybody believing in some aspect of it for something that many of them have no truck with whatsoever.... unless they're world leaders, in which case they're allowed to make it mean whatever they personally choose to.
For example, this is exactly the same kind of blurred thinking that many deeply unpleasant sorts do with their concept of Islam, going on a completely syllogistic mental journey from "some people who claim to be Muslims are terrorists" via "all Muslims who don't constantly condemn Islamist terrorists are sympathisers" and then "most Muslims are broadly not in disagreement with Islamist terrorism" and then ending up with "virtually all Muslims are in favour of terrorism". All falsely yet arguably 'plausibly' captured under the umbrella of 'Islamist terrorism'.
Closer to home, we see feminists who are keen to defend women's hard-won sex-based rights automatically painted as 'transphobic bigots' - #nodebate.
It's frighteningly easy to assert what a certain 'group' of people with one or more things loosely in common ALL 'believe' and then to condemn them as one for that imputed belief, whether it applies to them fully, partially, not at all or indeed if they have actively campaigned against those who believe it.