Display “Add to basket” and “Read more” buttons in the products shop page with woocommerce

Would something like this achieve what you are after? Could be refined more by using the default read more function rather than echoing it.

function add_extra_read_more_btn() {
    global $product;
    if ($product->is_purchasable()) {
        echo '<div class="woocommerce-LoopProduct-buttons-container">';
        echo '<a class="button product_type_simple" href="'.get_permalink($product->ID).'">Read more</a>';
    }
}
add_action( 'woocommerce_after_shop_loop_item', 'add_extra_read_more_btn', 9 );

function close_extra_read_more_btn_wrap() {
    global $product;
    if ($product->is_purchasable()) {
        echo '</div>';
    }
}
add_action( 'woocommerce_after_shop_loop_item', 'close_extra_read_more_btn_wrap', 11 );