In absence of a written constiution, the UK faces a period of uncertainty in respect of the implementation of Brexit by service of the required Article 50 notice. Interesting legal and political questions need to be resolved. If the ball is eventually going to be in the hands of Parliament in respect of the Article 50 notice, is it inevitable that they will never pass it and the PM of the day might be relieved of the duty to serve it?
This article provides a very useful assessment of the issues involved in this constitutional quagmire
https://ukconstitutionallaw.org/2016/06/27/nick-barber-tom-hickman-and-jeff-king-pulling-the-article-50-trigger-parliaments-indispensable-role/In this post we argue that as a matter of domestic constitutional law, the Prime Minister is unable to issue a declaration under Article 50 of the Lisbon Treaty – triggering our withdrawal from the European Union – without having been first authorised to do so by an Act of the United Kingdom Parliament. Were he to attempt to do so before such a statute was passed, the declaration would be legally ineffective as a matter of domestic law and it would also fail to comply with the requirements of Article 50 itself.