Hi, and welcome.
The British laws governing nationality are pretty complex, but I'll do my best! Be aware, though, that the law changes from time to time, so even if what I've written below is valid now, it may not remain so. And in any case, I'm not a lawyer - so I give no guarantees as to the accuracy of what I've written.
First and foremost, when it comes to dual nationality you need to consider the laws of both countries concerned. So you'll need to check out the nationality law of your children's other country - in your case, Australia. (You may also find it helpful to post on the relevant country forum here; other members may be able to give advice.)
The UK and dual citizenship
The UK has no bar on the holding of dual citizenship that I'm aware of - certainly not if you're entitled to your second citizenship by descent. (I'm a British/Irish dual citizen - both my father's parents were born in Co. Monaghan in Ireland.)
As far as the UK is concerned, if you hold British citizenship you never lose it
unless you specifically renounce it by a declaration made to the UK Home Secretary - or unless it's withdrawn because you've committed an act seriously prejudicial to the vital interests of the UK. The UK doesn't deem valid any renunciations made to other governments, eg the US.
British Citizens "by descent" or "other than by descent"
If either parent of a child born overseas is a British Citizen other than by descent, then that child is a British Citizen "by descent". British Citizens "other than by descent" generally means people who were born in the UK to British Citizens.
This is more than just a technicality. British Citizens by descent cannot pass on their British citizenship to their children, unless those children are born in the UK or "qualifying territories" (British Overseas Territories except for the Sovereign Base Areas in Cyprus).
Registering the birth of a British Citizen
You can register your child's birth (and thus citizenship) on the basis of either a parent's residence in the UK, or the family's (both parents plus child).
If you're applying to register on the basis of the parent's residence, it should normally be done within
12 months of the child's birth, though exceptionally the Home Secretary can grant an application up to the child's sixth birthday. However, this type of registration does not give the child the status of British citizen other than by descent. (You don't actually have to register your child to give them British citizenship - if they qualify, it's automatic - but it makes it easier for them to get a British passport if you do.)
If you want your child to become a British citizen other than by descent, then both parents and the child have to spend at least 3 years together in the UK first. Registration can take place at any time up to the child's 18th birthday.
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I hope this helps. As I say, this is my understanding of the UK law, but there's more information in the Home Office's guidance here:
BN4 - British Citizenship - children born outside the United Kingdom
You should check any areas of doubt with the Home Office direct or with the British Embassy, High Commission or Consulate -
and also with the authorities responsible for citizenship questions for your child's other nationality.
[Edited 20 Sep 07 - corrections to registration procedure: two types of registration, plus deadlines]