Paws, reading the start of your story about "Two section managers came and got me and took me to an office and said they weren't accepting my letter as they want to know why and won't let me quit until I tell them." was interesting. I can think of at least fours laws broken and an not surprised that Personnel were so cross. An Employment Tribunal would love them! Shame you didn't think to ask the "bosses" what procedure was being used to "not allow resignation unless ....." and how that fitted in Law, or did you enquire? I get very cross when large firms either use their "knowledge" to bully employees by inferring rights that do not exist and which is in fact abuse of power, and/or do not uphold their duty of care to employees who are almost certain to have less expertise in employment Law/rights. Ok, off Soapy's box ......
So who is this firm then that you still just about work for? It must be a chain if you have section managers. I had always assumed it to be a one man owned shop, but clearly not. They will have nothing to hide, being a "responsible employer" as they all claim