If you bank with HSBC, you can open a HSBC Australia account.
HSBC Bank, International Branch Tel: 020 7991 7278 (Local High Street Branches may not know about it)
Account Details at:
http://www.hsbc.com.au/personal/accounts/osa.html
The main Australian banks that facilitate overseas opening are:
Commonwealth Bank, Financial and Migrant Section, London EC4V 4HA, Tel: 0207 710 3990
ANZ Bank
ANZ account details
and
Westpac Bank -
Migrants page and
Westpac account details
HSBC charge no fees, and pay 4.75% on their transaction account.
Commonwealth charge either $4 or $6 per month, depending on the account.
ANZ access accounts charge either $2 or $5 per month
Westpac charges $5 per month for their standard account,
but allow 2 accounts for that, one of them being a savings account, paying reasonable interest of 5.8% pa.