Well, in the end it was a bit more complicated than I hoped. I decided to take out the black box and remove the broken-off connector from inside the hose so that I could glue the connector back on, only to discover that at some point in the past, someone had already done it! So the connector was totally mashed and the box and pipe had glue all over them. Anyway, we have a workshop where I work so I took the pieces in and one of the guys there helped me make a new connector and stick it on.
I have now put in the repaired part and all seems to be well again

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