I use GMX and can thoroughly recommend it. (It's the email arm of 1&1, which is a major player in the internet world so, unlike some smaller companies, it's not likely to suddenly disappear from the scene). It's 100% free and doesn't append advertising to either incoming or outgoing mail. (Just like here on AB, the only ads appear down the right-hand side of the web page). GMX can be accessed either via the web or by using a mail client (such as Outlook Express, Windows Live Mail, Thunderbird or phone apps).
To get an email address ending in '@gmx.co.uk' go here:
http://www.gmx.co.uk/
If you'd prefer '@gmx.com' go here:
http://www.gmx.com/
Icons on an iPad are assigned by the app that you're using to access your email, rather than by any particular email provider, so I can see no reason why using GMX would present any difficulties in that respect.