On the immigration side, there should be no issues. On a UK passport you don't need a visa to transit. You don't need a legal right to enter Australia and so issues you may have in getting one are irrelevant. So immigration is simply not part of your journey.

Ensure you meet this criteria however for transit without visa:
https://immi.homeaffairs.gov.au/visa...t-without-visa

MEL has a transit area and so no problems there:
https://immi.homeaffairs.gov.au/visa...alian-airports

I would not recommend seeking an ETA as advised above. It is guaranteed to be rejected and would only risk causing more issues. It would notify Australia that you are coming and suggests you intend to enter the country which you do not. In normal circumstances an ETA is nice to have for transit in case of flight delays. Not in your case, it's a liability.

The sticking point is the criminal side; Australia could stop you even if you don't formally enter the country if you have an outstanding warrant. Would they bother? Probably not, but they can. I can't really offer advice on the risk in this regard. I am not an expert or lawyer in any case.