is west wales suitable for growing an Australian tea tree?

You might be sable to get away with growing it in West Wales. in a sheltered spot. It can take a little frost . I found several trees that wont grow here will do well in West Wales. We had a cottage at Nevern in Pembs.

What's an australian tea tree?

Melaleuca alternifolia. It's the tree from whichTea Tree Oil (a natural antiviral, antibacterial, antifungal essential oil) is extracted.

Over here in Aus we love Tea tree everything, same with lemon Myrtle. You can get soap, tea, powder, lipbarm, you name it, in these flavours!

If you plant one where you are I would give it shelter like Poa annua says, and careful not to over water, because lots of plants over here are used to dry conditions.