Without more information, such as how your different veg have been growing, how water soaks in during heavy rain, what is causing you difficulties and what weeds predominate, I cannot answer for your allotment.
I see the phrase “hard pan” a lot and am intrigued by how it is different from a pan, which by definition is hard. Your crops and weeds are the indicator.
I suspect that someone on the allotment has worried you, from seeing that you are no dig.
But if you yourself are finding poor growth, despite your improvements with organic matter, then one loosening with a garden fork will break the pan. It can’t be very deep (if it is there) because rotovators, the main cause, do not pass more than 5-6in (12-15cm) into the soil.