If the page name and file name are identical, it'd probably be much easier to just do something like:
$valid = array('home', 'people', 'programmes', 'ethos', 'etc.');
$page = (isset($_GET['page']) && in_array($_GET['page'], $valid) ? $_GET['page'] : 'home');
include "includes/$page.php";
Also, not sure I understand your question/problem... can you explain a little more? What's happening versus what should be happening?
Otherwise, you can combine multiple cases using a single code block. Example using the present switch() setup in index.php :
switch($page) {
//Home
case "home":
//People
case "people":
//Programmes
case "programmes":
//Sales
case "sales_and_distribution":
//Ethos
case "ethos":
//Contact
case "contact":
$content = 'includes/' . $page . '.php';
break;
default: //If the variable didn't match any of the above cases do this.
$content = "includes/home.php";
break;
}