u/TronZ4

Hi, I'm travelling to UK/Edinburgh for vacation soon. Don't qualify for an ETA. Applied for new UK passport - status shows it was approved and has been sent - but won't arrive in time before I leave for Edinburgh. Travelling Chicago-Edinburgh on United Airlines next week.
Will I be able to board plane in Chicago ok?
Will I have issues when I go through immigration in Edinburgh?
Planning on taking copies of UK birth certificate, marriage certificate (proving my last name is accurate), photocopy of UK (old and expired) passport - which I no longer have as I had to mail it to HM Passport office with my application.
Any advice welcome! Thanks in advance.