If its Drupal 7 you need to theme your blocks. You can override that by creating a block.tpl.php file & place it where your html.tpl.php file resides.
Next goto http://drupal.org/files/issues/Core_templates_and_suggestions.pdf
to see what template suggestions you might need. You can also search drupal.org for more, bc your block.tpl.php file might be named block--%--.tpl.php < % denotes wildcard.
Next you will have to theme you block. You can control the HTML output with the $output variable, as well as classes and ID's. You have the option of generating classes and UD's statically or dynamically.
You could also do a theme preprocessing function (your_site_name HTML &vars function) in the template.php file.
Example for block.tpl.php
/* more code here, below outputs whatever you code here */
$output .= '' . $links['title'] . ''";