The following script is returning the wrong time after I call date_default_timezone_set("UTC")

<?PHP   
    $timestamp = time();
    echo "<p>Timestamp: $timestamp</p>";

    // This returns the correct time
    echo "<p>". date("Y-m-d H:i:s", $timestamp) ."</p>";


    echo "<p>Now I call 'date_default_timezone_set(\"UTC\")' and echo out the same timestamp.</p>";
    echo "Set timezone = " . date_default_timezone_set("UTC");

    // This returns a time 5 hours in the past
    echo "<p>". date("Y-m-d H:i:s", $timestamp) ."</p>";

?>

The timezone on the server is BST. So what should happen is that the second call to 'date' should return a time 1 hour behind the first call. It's actually returning a time 5 hours behind the first one.

I should note that the server was originally set up with the EDT timezone (UTC -4). That was changed to BST (UTC +1) and the server was restarted.

I can't figure out if this is a PHP problem or a problem with the server.