Adding a Table to the wordpress database

Try:

function vw_postcode_checker_create_db () {
    global $wpdb;

    // Create Table Name
    $table_name = $wpdb->prefix . "vw_postcode_checker";

    // Write Query to add table to database
    if ( $wpdb->get_var("SHOW TABLES LIKE '$table_name'") != $table_name) {
        $sql = "CREATE TABLE $table_name (
            id INTEGER(10) UNSIGNED AUTO_INCREMENT,
            postcode  varchar(250) DEFAULT ''  NOT NULL,
            area varchar(250) DEFAULT ''  NOT NULL,
            PRIMARY KEY (id)
         );";
        // Execute Query to Create Table
        require_once (ABSPATH . 'wp-admin/includes/upgrade.php');
        dbDelta($sql);
        add_option ('vw_postcode_checker_version', '0.1');
    }
}
// Register table function
register_activation_hook (__FILE__,'vw_postcode_checker_create_db');

Note the use of $wpdb->prefix and the closures after PRIMARY KEY (id)

https://codex.wordpress.org/Creating_Tables_with_Plugins