Customising the search function?

You can use pre_get_posts hoot to filter the search query to selected sectors only, something like this:

function Search_with_in_a_tax( &$query ) {
    if ( is_search() && isset($_GET['sector_array'])) {
        $tax_query = array(
             array(
                'taxonomy' => 'news',
                'terms' => $_GET['sector_array'],
                'field' => 'term_id',
              )
         );
         //turn it into a WP_Tax_Query object
        $tax_query = new WP_Tax_Query($tax_query);
        $query->set("tax_query", $tax_query);
    }
}
add_action('pre_get_posts', 'Search_with_in_a_tax', 1);

Update:
Put the code from above at the functions.php file of your theme and then you need to output the categories (sectors) as form fields inside your search form so try this:

<form method="get" id="searchform" action="<?php bloginfo('home'); ?>/">
    <div>
        <label for="s">Keyword</label>
        <input type="text" size="18" value="" name="s" id="s" />
    </div>
    <div>
        <label for="sector_array">Sectors</label>
        <?php
        $categories=get_categories(array('orderby' => 'name','order' => 'ASC'));
        foreach ($categories as $category) {
            echo '<input type="checkbox" name="sector_array[]" value="'.$category->cat_ID.'">'.$category->cat_name;
        }
        ?>
    </div>
    <div>
        <input type="submit" id="searchsubmit" value="Search" class="btn" />
    </div>
</form>