As a very dirty fix I added the following lines
$description .= "\nClient: " . $order->get_billing_first_name() . " " . $order->get_billing_last_name() . "\n";
$description .= "Email: " . $order->get_billing_email() . "\n";
$description .= "Phone: " . $order->get_billing_phone() . "\n\n";
just before
$edit_booking_url = admin_url( sprintf( 'post.php?post=%s&action=edit', $booking_id ) );
in
./wp-content/plugins/woocommerce-bookings/includes/class-wc-bookings-google-calendar-connection.php
Seems to work ok but did not test intensively…
Cheers,
Holly