By putting the data into a form, I was able to make the body around 1800 characters long before the form stopped working.
The code looked like this:
<form action="mailto:[email protected]">
<input type="hidden" name="Subject" value="Email subject">
<input type="hidden" name="Body" value="Email body">
<input type="submit">
</form>
Edit: The best way to send emails from a web application is of course to do just that, send it directly from the web application, instead of relying on the users mailprogram. As you've discovered, the protocol for sending information to that program is limited, but with a server-based solution you would of course not have those limitations.