I believe this is inaccurate. "No deal is illegal" is a gross simplification.
What the parliamentary No Deal bill states is that if a Brexit deal isn't agreed in parliament by October 19th, or if parliament has not given its consent to a No Deal Brexit by then, then the government must send a letter to the President of the European Council requesting an Article 50 extension until 31 January 2020, and if the European Council agrees to an extension to the 31 January 2020, then the Prime Minister must immediately accept that extension.
The bill does not provide a legal pathway if the EU rejects the request for an extension.
In such circumstances, I believe a No Deal Brexit would remain the default position, and parliament would have to call a vote to revoke Article 50 outright as the only means to prevent it. Whether they would go that far, I'm not sure.
It's also probable that the EU would agree to a further extension if we had passed a vote for either a second referendum or a General Election.
Even as an ardent remainer, I'm angry with the Lib Dems and Labour that they've left this possibility on the table.
They had the opportunity to make their case to the British people through a General Election and, if they won it, permanently remove the possibility of a No Deal Brexit. But they were too scared of losing to do so, and decided to play games instead. Which could now blow up in their, and everyone who opposes leaving the EU without a deal's faces.