HTML alone cannot do this - you will need to use either PHP or Javascript. The fwrite function in PHP can help you acheive this.
PHP Code:
$file = "formData.txt";
$handle = fopen($formData, 'w') or die("Cannot open file - check write permissions!");
$formData = $_POST['fieldThatHasTheData'];
fwrite($handle, $formData);
fclose($handle);
You would need a previous file that has the form data. I would certainly use post as the get method, although you could use get.