In Australia and New Zealand they speak Australian and New Zealand English. You must have had your ears well blocked when you visited the UK is you think they are close to British English -- though if you spent most of your time in the UK watching soaps on TV then you have an excuse.Don't you realise that all other countries (except Canada) where English is spoken as a first, or global language use BritEng? Australia and NZ may not have big numbers, but what about India, Singapore, Malaysia and many countries in Africa, such as Nigeria, Ghana, Egypt, South Africa? All together these double the number of US and Canadian speakers.
In India they speak Indian English, and rascal who says otherwise should be severely apprehended.
In South Africa they speak South African English.
It is foolish to put "people who speak English as a global language" in the same boat as native English speakers. Speakers of Chinglish and Spanglish do not have a homogenious variety of English - they merely have different levels of imperfection dependent on how much or little they are influenced by their native language.
In countries where English is used as a bridge language between different language groups the question of their status is a thorny one. Nevertheless I think it is more useful to think of Malay or Malay Chinese speakers of English as being on a par with Spanish, French, Indonesian or Russian speakers of English, rather than members of a Creole community.
As for the variety of English taught, I would say that normally depends on the geographical area, and the origin of the speaker. In most of Europe, British English is the norm, whilst in Central and South America it is almost universally American English. In Asia there is a split, but the American variety has greater peneitration, and of course one can be sure most Koreans and Taiwanese know all the technical terms for ice hockey.