So, what do you do when you get this from your logs?

I/O error reading the header from the binary log

Obviously the binary logs are broken, or at least the last one is. They are usually located in /var/logs/mysql/ and you should not start copying over some old logs with the new name because that would just not make it right, so the solution is,

1. read your logs and see which *.bin file is corrupted
2. delete it
3. open /var/log/mysql/mysql-bin.index and delete the line with the bin file on it.
4. Restart mysql

et voila 🙂