I have been unemployed for a long time and the only experience I have on my CV was working in retail at Next on a very short temp contract (month). I know that’s terrible but I really struggled to find another retail job due to bad anxiety, as well as not having enough experience for other retailers. Even my local charity store, Barnardos, said they wouldn’t be able to let me volunteer without having 2 references.
I recently was interviewed for an entry level job in a bank and some how was successful. I was given an informal offer over the phone, however was told the offer was subject to references. 
I’m not even sure whether my only employer, Next, would be able to provide a reference as they have a very high staff turnover so will have long forgotten who I am. I can’t even remember my line manager’s name, I don’t think we were even introduced as it was such a short contract.
I’m unsure what else I can do to get a reference, I know academic references are sometimes accepted but I don’t feel as if I was close to any teachers. Also, I’m not sure if my school / college would find it bizarre I’m requesting a reference at my age 
(I’m mid 20s)