There is a difference between an account denominated in GBP and a UK bank account. Most of the replies here relate to accounts denominated in GBP (and/or other currencies). Another option of that nature is a HSBC Global Everyday account (which I use). The problem with these options (as far as I understand it), is that these accounts can't accept standard domestic transfers from overseas accounts - they are really just a means of converting Aussie $ into another currency and then spending it/withdrawing it while overseas or shopping online.
I gather the OP is looking to open an account in the UK, which is quite different. I agree with Duffa and MartinMemo that it's difficult if not impossible to do that if you don't actually live in the UK. Even if you are a UK citizen, I believe you need a UK address in most cases.
HSBC might be an option. One of the advertised HSBC Premier benefits is "Fee-free International account opening and HSBC credit history transfer available in over 35 countries for Premier customers." However, I don't know if this is aimed at customers who are moving overseas, as opposed to Australian resident customers who just want to open an account overseas. Also, HSBC Premier is only available if you meet certain criteria, for example having a home loan with them over a certain amount.