Do NOT keep your Qantas credit card. You will probably be hit with a 2.75% foreign currency fee every time you use it (this may be a hidden fee, in that it is built into the exchange rate and does not appear on your statement) in the UK.
Get the BA Amex and either a BMI Mastercard or Tesco Visa (for BA Miles) as back up. There are also UK-issued Marriott Rewards, Priority Club and Hilton Visa / Mastercards if you are a keen hotel points collector.
Citibank in the UK does a Sterling AA card, but BA Miles are far more useful for a UK resident since you can use them for upgrades on BA flights, as well as getting the '2 for 1' voucher which comes with the BA Amex.