This resulted in the slave error log having a line saying:
[ERROR] Got fatal error 1236: 'Could not find first log file name in binary log index file' from master when reading data from binary log
Don't panic. You need to manually edit the master's HOSTNAME-bin.index file and change all ./ relative paths to the absolute path (matching the ones created since the upgrade). Don't do this with the master running for obvious reason. Once you've restarted the master, restart the slave and the slave should catch up. Well, it did for me.