function wpse_check_email_domain($errors, $sanitized_user_login, $user_email) {
    $start = strpos($user_email, '@uniname.ac.uk');
    if(!$start)
        $errors->add('ERROR', 'Only users with "@uniname.ac.uk" email domain can register!');
    return $errors;
}
add_filter('registration_errors', 'wpse_check_email_domain', 10, 3);