Naturalised citizen entering UK using old passport

I assume this must be a common question but I haven't seen an answer anywhere.

I have just become a British citizen, attended the ceremony and received my certificate. I have also retained my original Australian citizenship and passport.

I need to travel briefly outside the country in a few weeks, and although I could apply for a British passport immediately, I probably wouldn't receive it before I leave.

When re-entering the UK, would there be any complications if I use my original Australian passport and BRP? Should I bring with my a copy of my naturalisation certificate?

Should be fine but carry your naturalisation certificate with you as ILR BRPs are now no longer valid once citizenship is complete.