I've not done so recently, but have had no problems in the past calling 0800 numbers from outside the UK using +44 from the local country's phone service. These calls were charged like calls to ordinary UK numbers.

Does the Three UK service offer WiFi calling and is that being used? It may possibly work when a call routed through an Australian mobile tower might not work.

Otherwise I can only suggest trying as many different BA numbers as possible and asking to be transferred.