A number of Parliamentary committees have opened inquiries into legal issues arising from Brexit:

The Foreign Affairs Committee of the House of Commons is conducting an inquiry into the following legal issues:

• Whether all directly applicable regulations that currently apply to the UK can be transposed into UK law in a single Act of Parliament.
• On what terms will the UK and EU trade at the end of the 2-year negotiating period mandated by Article 50 of the TEU if no deal has been agreed between the UK and EU on the terms of Brexit, and/or on the future relationship between the UK and EU.

The Joint Committee on Human Rights has launched an inquiry in to the human rights implications of Brexit, including for:

• the protection of private and family life for EU nationals currently living in the UK and UK nationals in other member states.
• human rights clauses in trade details.
• EU law rights including labour rights, disability rights, rights to freedom from discrimination.

The House of Lords Select Committee on the Constitution has published a report on Article 50 (on 13 September 2016) which comments on whether an Article 50 can be made without Parliament and whether it can be unilaterally withdrawn by the UK.  The report concludes that Parliament should assume that it cannot be withdrawn, and that:

“It would be constitutionally inappropriate, not to mention setting a disturbing precedent, for the Executive to act on an advisory referendum without explicit parliamentary approval – particularly one with such significant long-term consequences. The Government should not trigger Article 50 without consulting Parliament… In our representative democracy, it is constitutionally appropriate that Parliament should take the decision to act following the referendum.  This means that Parliament should play a central role in the decision to trigger the Article 50 process, in the subsequent negotiation process, and in approving or otherwise the final terms under which the UK leaves the EU.”

See also the report of the House of Lords Select Committee on the EU’s reports on the process of withdrawing from the EU and on the role of Parliament.