Lifted my onions - what now

I have had a lot of problems with white rot in different places on my allotment. I only took it over in Jan of last year and was told it had not been tended for 3 or 4 years. However I have now found extensive white rot in 3 different beds.

After seeing a fair number of my onions falling over - I lifted some and found most had almost no roots and were suffering from the start of white rot. I decided to lift them all before it destroyed the actual bulbs. Should I leave the greenish leaves on until they wilt and go brown or do I cut them off. I read on another thread that cutting them off early gives yet another route for infection to get into the onion?