Nope, the AND keyword only should be needed with clauses such as WHERE.
Also that code probably wouldn't do anything since you are saying you need to update the username where all of those variables are equal to the post data (I presume).
mysql_query("UPDATE `users` SET username='$username' , street1='$street1' , street2='$street2' , town='$town' , county='$county' , postcode='$postcode' , country='$country' , email='$email' WHERE username=$_POST[id]");
There ya go, that should work for ya.
You should also add the WHERE clause for the username or something like I tried at the end there. I'm not quite sure how you are verifying or getting which user to update, but that's how you would do it.