That's cutting it a bit close for me. If everything was on time 30min would give you enough time to deplane, walk straight to your next gate, and board. If a butterfly flaps it's wings in the Amazon then you're going to miss your connection.

I would want closer to one hour to make the connection, unless missing your second flight wouldn't cause any major issues.

Edit: i'm assuming you're on BA/US. Remember there's a BA PHX-LHR non stop most evenings if you need it.