Wordpress - Woocommerce - Add a product to cart programmatically via JS or PHP

OK so here's how I solved it in the end. A quick and dirty example, uses JQuery.

<a id="buy" href="#">Buy this!</a>
    <script>    
       $('#buy').click(function(e) {
          e.preventDefault();
          addToCart(19);
          return false;
       });    

       function addToCart(p_id) {
          $.get('/wp/?post_type=product&add-to-cart=' + p_id, function() {
             // call back
          });
       }
    </script>

This just makes an AJAX GET request to the cart url

/wp/?post_type=product&add-to-cart=[PRODUCT_ID]

In PHP I managed to do it this way:

global $woocommerce;
$woocommerce->cart->add_to_cart($product_id);

The method is in woocommerce/classes/class-wc-cart.php:

    /**
     * Add a product to the cart.
     *
     * @param string $product_id contains the id of the product to add to the cart
     * @param string $quantity contains the quantity of the item to add
     * @param int $variation_id
     * @param array $variation attribute values
     * @param array $cart_item_data extra cart item data we want to pass into the item
     * @return bool
     */
    public function add_to_cart( $product_id, $quantity = 1, $variation_id = '', $variation = '', $cart_item_data = array() ) {