See the following:
IDIs (casework instructions) for UK Ancestry applications
Immigration Rules relating to UK ancestry
Please note that if you were adopted before you were 18, you can use your adoptive ancestors/relatives as well as your biological ancestors.
If you are in the UK, you could pay a visit to the National Archives to find evidence you may need:
National Archives - about us
Or order any certificates from the register office (more likely):
http://www.direct.gov.uk/en/Governmentc ... /index.htm
If you do not have UK ancestry that allows you to get to the UK, then there are work or study routes:
Tier 2 - no degree needed - but you need a job offer from a licenced employer
Tier 4 - as a student - this will be expensive
There is also the Youth Mobility Scheme in Tier 5 that is open to Australian nationals under 31. There is a quota each year, Japan's has run out so bear this in mind:
Tier 5 - YMS
Who can apply under the youth mobility scheme?
To apply under the youth mobility scheme, you must be a national of a country taking part in the scheme, and have a valid national passport from that country, which will be all the evidence you need to show that you are sponsored by the government of your country to apply for a visa under the scheme. (British overseas citizens, British overseas territories citizens and British nationals (overseas) can also apply under the scheme and do not need to be sponsored.)
Who can apply under the youth mobility scheme?
To apply under the youth mobility scheme, you must be a national of a country taking part in the scheme, and have a valid national passport from that country, which will be all the evidence you need to show that you are sponsored by the government of your country to apply for a visa under the scheme. (British overseas citizens, British overseas territories citizens and British nationals (overseas) can also apply under the scheme and do not need to be sponsored.)
You can apply if you:
are a citizen of a country taking part in the scheme or a British overseas citizen, British overseas territories citizen or a British national (overseas);
are 18 years old or over when your visa lets you come to the United Kingdom (becomes valid) and under 31 years old when you apply;
have £1,600 in available maintenance (funds) when you apply .
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Who cannot apply?
You cannot apply if you have:
children under 18 years old who are either living with you, or you are financially responsible for;
been in the United Kingdom at any other time as a working holidaymaker or under the youth mobility scheme.
You cannot apply for the youth mobility scheme if you are already in the United Kingdom.
If you qualify for that, you would have to apply in Australia. You can also work for the full 24 months. This would give you time to "test the waters" relationship wise and then think if you want to get hitched or apply as an unmarried partner (having lived together for 2 years) - you would need to apply for something else before your leave runs out.
Australia also has a scheme similar to the YMS, perhaps that is an option to stay together.
All the UK options will involve you returning to Australia and applying to come back. You cannot extend a visitor visa unless something really awful has happened. You cannot switch to something else in the UK from a visitor's visa unless you can show it would breach your human rights or something like your country disappearing under a volcano.
You could also leave the UK and come back as a fiance or spouse as Wanderer said!!
There are other options, but not widely used, such as charity work, working in your High Commission or joining the British Armed Forces and so on.
You haven't given us much info, so I hope this helps.