A question about work references?

Honestly yes but you should have reported the bullying before resigning, i wouldn't know what to do but i would still ask for a reference and if they refuse still let it be known in the job interview that you asked for one but were refused it. They can ask for one themselves but generally companies don't take kindly to people who resign or leave for what may seem like an insufficient reason to them. If the interviewer asks why did you resign? tell them the truth. Don't lie or try to make up excuses.

They have no obligation to give any reference - no employer does, contrary to popular belief.

In the circumstances I'm not sure you would want a reference, since it might say "resigned without notice" which any future employer will probably quiz you about. However, as long as you are truthful there is nothing to fear, as long as you resist the temptation to criticise your former employer.

You should have raised a grievance rather than simply walking away, but you can still claim constructive dismissal and bullying/harassment at an Employment Tribunal.

Links below for more guidance.

if you want to get references from them, make sure you have the incident documented with their HR manager. but of course, the area manager will be unlikely to provide you with the reference.

I definitely would not use them, it most likely will not be positive feedback.