Hi! Have been in England since Sept, and just got married Nov 5!

Read about the new regs regarding amending passports (that they won't do it anymore due to heightened security). My question is this. Since I need to get a new passport when I change my name, should I get my new passport first, and then apply for my FLR? I wasn't sure what the FLR was (stamp, or like my fiance visa), and I thought it might alieviate needing two passports (one w/ flr and new one w/ new name).
My finace visa is good until Feb 2006, and I'm not in a rush to be eligible to work. So time-wise, I do have the time to get my new passport first. But since FLR is crucial to me (moreso than changing my name) I wanted to know from those who've gone through the process what they recommend. I'll be mailing my application for my FLR.
Thanks for your help!
Rebecca