MCT Int to Int at PHX
 

Arriving on BA from LHR and leaving on AA to MEX - AA are changing the flight times around and it's currently an 80 minute connection

Is this doable? I presume I have to go through immigration, customs and security or is Int to Int possible without clearing US soil at all?

I'll be hand baggage only if that helps with timings

According to ExpertFlyer International-International MCT is 60 minutes
So 80 minutes should be OK

In my experience, at other US ports, it doesn't matter whether you have checked baggage or not - the baggage will be there by the time you get through immigration and it's just a matter of walking it through Customs and then dropping it off

You should be OK. But I'd suggest you get a seat near the front of the BA aircraft so you can be one of the first through immigrations and customs.
I have cleared PHX immigration many times, and it is usually pretty quick.
Also, in case you for some reason can't get your AA boarding pass during check-in in London for your PHX-Mexico flight, one can usually be obtained just before security at one of the small kiosks. No need to walk downstairs to the check in counter.

There is no such thing as transit in the US. There are some modified procedures at some stations, but PHX is not one of them. OP will be processed through immigration, pick up his bags, move them through Customs and drop them, process through TSA and head to his gate.

Does PHX have the oneworld express connection service?