I would speak with your GP about getting the gene test done, and go form there, and if he laughs at you, tell him you don't pay for that, you pay him to give you the referral you ask for. If he refuses, find one that will. It is not so rare these days for women at risk to have double mastectomies without any sign of cancer at all, based purely on family history and presence of the gene or not.
A GP can't just write a prescription for a genetic test. You need to go through a genetics clinic. This is because genetic info is special in that you knowing your results may have implications for other family members.

There are a number of genes that can increase your risk of cancer. For a non-affected person to have predictive genetic testing, the family genetic mutation (from one of the family members who has had the genetic cancer) needs to be known.

Has your Mum or Aunty had any genetic testing? How old were they when they were diagnosed? Are there any other family members with other cancers? What types? Did your Mum have cancer in one breast or two? All these questions can help determine your risk, which will affect what options (publicly funded) will be available to you. (i don't mean write the answer here, but just letting you know things that will be important)