>>>gmx sounds dodgy, they want my email address and password
GMX is run by one of the biggest and most well-respected internet companies in the world, 1&1, who provide internet facilities (such as web design and web hosting) to many major multi-national companies. They're hardly cowboys (and they're far less intrusive than either Microsoft, who run Outlook, or Google, who run Gmail)
To use GMX you first need to create an account with them (giving you an email address ending in @gmx.co.uk). You do that by clicking on 'Sign Up Now' and entering the relevant details (i.e. selecting a username and password). Once you got that account you can use that email address and simply forget about your Hotmail one or, more likely, use the 'Mail collector' facility to retrieve your mail from the Hotmail/Outlook server. Obviously you have to enter your Hotmail/Outlook address and password at that stage; if not, anyone would be able to get your mail that way!