Will a diagnosis of psychosis ban me from getting my recreational pilots license or my private pilots license?
Well, according to the CAA:

Class 1
(a)  Psychotic disorder
A history of, or the occurrence of, a functional psychotic disorder is disqualifying unless a cause can be unequivocally identified as one which is transient, has ceased and will not recur.
Class 2
Psychotic disorder
A history of, or the occurrence of, a functional psychotic disorder is disqualifying unless in certain rare cases a cause can be unequivocally identified as one which is transient, has ceased and will not recur.

Discussion on another forum suggests that generally speaking they will want the pilot to be off all psychotropic medication for a period of time (1-2 years) without any recurrences but they will generally allow a pilot to be on medication for depression.
I would recommend you work with an appropriate mental health expert in resolving your condition, so that you can be sure future episodes will not recur, you can then hopefully ascertain to yourself and to your medical examiner that your episode was transient, so that you can continue your pursuit of your PPL.
Remember in the worst case scenario (your condition does not pass), even if you cannot get a medical, you can still fly a plane. You just can’t solo. You can fly with a flight instructor or a certificated pilot. And you can fly a single seat ultralight with no certification. So you will still get to fly, don't worry.
Good luck, I'm sure you can do it.