Similar situation. My Italian partner (British citizen due to her mother being born here) is here in the UK (since Jan) and needs to go back for exams in 2 weeks. Her Italian passport is with the Durham passport office as a supporting document (documents signed for by the office on March 25th, application processing since April 13th).
She only has an Italian ID card, but isn’t sure if this is sufficient to *leave* the UK. The last thing we need is for her to arrive at the airport and Ryanair say “no”.
