After doing more googling specifically around AjaxControlToolkit and IE11, I found a number of people complaining about problems with the current version of ACT (the Sept 2013 release) and IE11.
It seems the problem is with .net failing to identify IE 11 as an IE browser, causing various AjaxControlToolkit features to fail.
The workaround I'm using at present is to add the X-UA-Compatible http header to our site, to force IE11 to process the page with in IE10 mode.
<meta http-equiv="X-UA-Compatible" content="IE=10">
There is also this .net4 hotfix from Microsoft which should fix the problem completely when applied to your web server.