No need to get feisty.
You need to understand, mod_rewrite doesn't actually change the underlying urls, so your form will still need to have its action point to wherever it need be whether that be a nice neat url that gets rewritten to something else, or straight to that something else).
Leaving your action as is in your last post, you simply need to rewrite /mysite/testwebsite.co.uk/Search/ to /mysite/testwebsite.co.uk/index.php and pass the querystring params along with it. Something like.....
RewriteRule ^mysite\/testwebsite.co.uk\/Search$ mysite/testwebsite.co.uk/index.php [QSA]
ps: Those urls don't exactly look valid. Do you access your site via http://somedomain.com/mysite/testwebsite.co.uk ?