We misplaced our EHIC cards and I rang the phone number given on this link (under FAQ - also the same number previously provided by David) and the replacements arrived within a few days.
It was however back in early May so they may not have been as busy as they are now.
A couple of weeks ago we did an online application for a couple of friends of ours who didn't realise about the EHIC replacing the E111 until she went into the Post Office.
They didn't have enough time to apply either by post or phone.
I did the application on the Wednesday evening, the cards came through the following Tuesday - in time for their holiday, so a pretty good service.
https://www.ehic.org.uk/InternetResPROD/home.do
Polly