You can use both former and old in BrE.I moved to another apartment. Could I say "the old apartment" to refer to the apartment I just lived in? Or "the former" apartment? Thank you.
"The former" would be better.
Although "the old" is correct, it means it is not new or modern.
I am not sure, but I think there is something wrong with " I just lived in" . Could you rephrase your question?