At present, the UK parliament is attempting to pass legislation that would require Boris Johnson's government to take action to avoid a no-deal Brexit scenario. For the purposes of this question, I am assuming such legislation is passed and thus it would be illegal for the government to allow no-deal Brexit to occur.
There have been suggestions that the government might choose to simply ignore such legislation. The treaties around Brexit stipulate that Brexit will happen by default, unless the government gives notice to the contrary. Obviously, by the time it became apparent that the government had failed to give such notice, Brexit would have become a fait accompli. This would be an illegal act under UK law, but presumably UK judges would have not have jurisdiction to compel the EU to re-admit the UK to EU membership.
What (if any) legal recourse would be available in such circumstances?
Edited to add: As noted in comments, it is quite possible that the government might seek an extension in accordance with such legislation, but be unable to secure the EU's agreement. However, for the purposes of this question let's assume that the government makes no attempt to do so.