I did two things to fix this problem. The first was to start using operational accounts instead of personal accounts for work directly related to the website. The entire web team have access to these accounts, meaning if someone is away nothing gets missed.
The second thing was to set up an out-of-office reply. The point of this is NOT to tell people when I am back. The point is to provide the email addresses that they should be using instead, and saying who is on-call.
The other thing that I added was a note to say that I was not going to read ANY of the email received while on holiday - so if it was important, please resend the email when I got back.
This message caused a bit of controversy, but the effect was dramatic. While on holiday I knew I could completely forget about my email because those sending the mail would do the work for me! They would decide who to contact instead (from info in the reply), or to resend it later.
That first year I took a hard-line - emails were trashed automatically when received. Over 1,000 were in the trash when I got back. Only one 'important' email was resent. The second year it was about 200.
Now things have settled down I don't trash emails anymore, but I still have an auto-response stating who to contact for operational issues. And holidays are so much more relaxing.