Does your host have the webserver configured to parse .html pages for PHP? This is usually not a good idea (potential slight performance penalty), but at least you'll be able to use PHP as usual.
Does your host allow .htaccess pages? If so, you may be able to do some URL rewriting.
If not, then you should insist that your host allow the index page to be index.php
If they refuse, perhaps it is time to change host, or ask them to advise you on the matter.