As Simon said, they all operate independently unless you have private banking. Go with any account that has a cheap monthly fee and use TransferWise to make the funds transfer. They are wicked cheap especially for GBP to and from AUD.
If you are planning to close your UK accounts then go with a bank with super low foreign cash-out fees using your Australian debit card. I use Citibank Plus which is pretty awesome for this (but sucks for customer service).