Rete

You were told this several times in this thread about the quickness of return of the UK Passport. See Pulaski's post #2 for example and Bob's just after it.

petitefrancaise

I would also be concerned if I didn't have proof of my immigration status on me at all times. Maybe it's because I also live in a border State?
Anyway, in your position I would keep a print out of my i94, a photocopy of my passport with the visa stamp page and the actual passport information in it showing expiry date, some kind of print out of the passport application sent off and keep your AZ driver's license on you as this probably indicates your status ( it does in TX) .
FWIW, my ex went through a CBP control post without his GC - they took his DL and checked him in SAVE and then issued him with a letter which stated that he is legally supposed to keep the GC on him at all times. That's it.

tht

If you are that worried, fly to London, you can do a same day renewal at the Victoria passport office with an appointment.