Obsolete apple ID holding my phone hostage

Hi all. I am in need of some help. A few years ago when I left a job, the day I was leaving i realised that my apple account was set up with my work email address. In a panic I quickly changed my apple ID online to an email address I would be able to use and that was that.

Little did I know that from that day onwards I would be plagued by this with all iphones I have subsequently had.

Basically, iCloud on my device is still set up with my old work email (that now neither exists nor would I have access to) - I am unable to log out of iCloud on my phone as it says firstly that the password is incorrect and if I use iForgot it then says the apple ID doesn't exist (which is true!)

I've found some docs online where people have had this same problem but these are a couple of years old so the solutions don't seem to work for me (i.e. logging into apple account, changing email to the old one....this is where it stalls as it sends a code to the old non existent email address and therefore I can't verify).

I can't believe that I am alone with this problem and there must be some way of sorting it out (without wiping all data from my phone!)....

As it stands I have a phone which requests the password for my old ID around once every second!! It is driving me nuts, making my phone unusable and making me hate it!!

Anyone???