Hi
We made the same move a couple of years ago (permanently), fortunately just before the UK exchange rate tanked!
Re bank accounts. We used the Commonwealth migrant service, which gave an account in London and Sydney - v useful for transfers.
We have UK & Oz addresses, and so have kept our UK Amex (no BA Exec Club out here) which we use in UK and added a Qantas Amex for local use. Have used 2for1 from UK card for trips back - obviously requires planning next trip at same time as round trips must originate London unless just use one way LHR/SYD. As you say, availability for 2for1 is tight but LHR/HKG usually wide open & we have managed to use voucher to route LHR/HKG & then SIN or BKK/SYD on BA miles (for same as LHR/SYD fare) with a cheapie on Jetstar or similar to cover the middle sector. Alternatively, just use your 2for1 to get as near to Oz as possible..e.g. routing possibilities incl LON/MRU on BA then MRU/SYD on Air Mauritius who had a cheap biz fare last time we looked.
Re removals. We used Pickfords - excellent service, took around 6 weeks and no problems at all - they packed & unwrapped everything so little for us to do!
Re accommodation. Prices in SYD still high as no housing crash yet (and an Aussie obsession with putting money into investment properties). Look at realestate.com.au & domain.com.au.
Re cars - carsales.com.au is a good starting point, or most dealers have ex demo cars at a good discount.
Best of luck!