Just looked. There is a sequential six digit cheque number. Not long enough to be unique by itself. However, it works with the sort code and account number. The combination is unique.IIRC all cheques have a unique reference number.
As I recall, my cheques started at 10001, with the sequence maintained between books. I have no idea what would have happened after 999999. (That would hav been a lot of cheques for a personal account.)