What could be the equivalent term in British or Australian English to the American English word “hillbilly”?
In Wikipedia, “hillbilly” is defined as: … a term referring to certain people who dwell in rural, mountainous areas of the United States, primarily Appalachia but also the Ozarks. Owing to its strongly stereotypical connotations, the term is frequently considered derogatory, and so is usually offensive to those Americans of Appalachian heritage.
I am looking for a term of equivalent meaning denoting the highly loaded emotional characteristic.
In British English there is the word yokel which has much the same pejorative overtones.
yokel noun
an uneducated and unsophisticated person from the countryside.[ODO]
While I'd agree that Andrew Leach's answer yokel is a good word for this, perhaps you could also (for British English) consider bumpkin:-
An awkward, unsophisticated person; a yokel.
The previously-mentioned terms bumpkin (“a yokel; a clumsy, unsophisticated person)” and yokel (“(pejorative) An unsophisticated person”, also “A person of rural background”) both appear in the British-equivalent-of-redneck virtuallinguist link given in a third answer. The linked page also states that “The words hick and hillbilly are used too (also pejoratively) but not very often”, and it goes on to mention slightly-less-relevant terms chav (“(UK, pejorative, offensive) A working-class youth, especially one associated with aggression, poor education, and a perceived "common" taste in clothing and lifestyle”) and pikey (“(UK, pejorative) A working-class (often underclass) person; can vary from specifically Irish Travellers to gypsies or travellers from any ethnic background, but now increasingly used for any socially undesirable person, with negative connotations...”), besides some dialectical or little-used but perhaps well-known terms like Scottish heuchter-teuchter and Irish culchie (“(Dublin, slang, pejorative, offensive) A rural person”) and some more-general terms like provincial and parochial.
However, the previous answers and the virtuallinguist link fail to mention the noun rustic, which means “A (sometimes unsophisticated) person from a rural area”. Wiktionary illustrates it via the following quote from Arthur Conan Doyle's story Sir Nigel:
The King looked at the motionless figure, at the little crowd of hushed expectant rustics beyond the bridge, and finally at the face of Chandos, which shone with amusement.