I'm due to go to the states at the beginning of April and have just damaged my passport. The luggage tag thing they give you when checking in (the sticky end off the one they wrap around your suitcase) from my last flight was stuck into the 'observations' page of the passport and as I've tried to remove it it has torn off the top of the paper. I'm worrying it's not going to go down well at immigration and so wondering if I have time to get a new passport in time 
I know I can go for an urgent appointment, but it's double the cost and I could do without that. Has anyone recently got a new passport and can tell me how long it took - am concerned brexit nonsense could be slowing things down... thanks!