Sounds like broad bean rust or chocolate spot, both fungal diseases which are more likely to affect broad beans in an enclosed space like a greenhouse where there is higher humidity. However, these mostly affect the plants once they are older and if you have been successfully harvesting them for a couple of weeks, it seems likely that there aren't too many more to come, as broad beans have a short harvest period.
You sound to have done far better than me as the broad beans in my polytunnel have mainly failed to set, due either to cool conditions or a lack of insect pollination.

Another GoYer has chocolate spot on their broad beans and, in the UK, there is no treatment available to amateur growers. Our broad beans are barely in flower yet later than usual but I am putting it down to the weather.

Thank you for your help, it is always good to know excatly what the problem is!