BBC Radio 4
Ms Fairbairn's debating partner on the Today programme was pro-Brexit economist Gerard Lyons who says a no-deal Brexit is only a plan B, but nevertheless a lot of sectors, including financial services do have contingency plans in place.
Mr Lyons said if a no-deal Brexit were to happen it would just be "a stepping stone" to a free trade agreement.
Whoever is the next Prime Minister “we need to focus on the UK's imbalanced economy” he argued.
"In my view, these challenges would be better addressed outside (the EU) and to make a success of Brexit we really need to focus on investing more in infrastructure and getting incentives right.
"The CBI remember was among "project fear" three years ago and since the referendum we’ve seen one million jobs added to the economy," he said.
BBC Radio 4
A no-deal Brexit is just "not a responsible strategy", CBI's director general Carolyn Fairbairn tells the Today programme. She says companies large and small across the country are calling for it to be ruled out.
She says there are 150,000 business with no strategy in place to cope if it happens.
"How can you be prepared for £20bn of increased customs costs? How can you be prepared for tariffs rising overnight?"
"Just look at what is happening in our economy: we’ve had four quarters of falling investment with company headquarters - Sony and Panasonic - leaving the UK. We have to listen to the evidence that’s coming through."
"No deal should be an option that is not even considered."
BBC Business Editor
British business has issued a challenge to the next Prime Minister to prove that the Conservatives are the party of business. That can only be achieved, says the CBI, if the next leader commits to leaving the EU with a deal.
The lobbying group insists that firms large and small are clear that leaving the EU with a deal is essential to protect the economy, jobs and living standards.
However, of the 12 candidates (so far), at least half say they are prepared (in fact some of them are determined) to leave the world's largest trading bloc as scheduled at the end of October - with or without a deal in place.
That includes the current favourite, Boris Johnson who, when foreign secretary, had a message for business leaders during the Brexit negotiations that ended in "ck" but wasn't "back".
BBC Radio 4
Sir John Hegarty, eminence grise of the advertising industry, is viewing the Conservative Party leadership contest from the point of view of branding for BBC Radio 4's Today programme.
By campaigning for a no-deal Brexit, which many companies are strongly opposed to, he argues that "as a brand they're destroying one of the things that is their main appeal" - their close relationship with business.
"Imagine Jeremy Corbyn got up and said 'I've thought about the NHS I think we should privatise it'."
"In a sense this is what the Conservatives are doing - they're destroying what they're about."
He says by vacating the centre ground, the main political parties are "creating an opportunity for another brand to come in occupy that middle space".
Some reaction to that CBI report which suggests UK services firms are feeling the heat.
Chris Sood-Nicholls from Lloyds Bank Commercial Banking says services businesses are facing "a mixture of long and short-term concerns".
He says: “It’s not all bad news though. Some tech and health firms appear to be doing well at the moment, while there are also some professional services businesses that typically prosper during times of change or uncertainty.
“But these bright spots are being outweighed by the fall in sentiment among other business and consumer services firms."
Firms in the services sector have reported falling profits in recent months, according to a new study from business body the CBI.
Its research suggests business conditions fell "sharply" in the quarter to May. It added that declining optimism was affecting firms in hotels, restaurants, travel, leisure as well as those in professional services.
And Anna Leach, the CBI's deputy chief economist, said Brexit "paralysis" was continuing to take a toll on the UK's services firms.
She warned: "Profits, optimism and investment spending are falling sharply amidst a torrid operating environment.
"Politicians have wasted six critical weeks, allowing uncertainty to tighten its stranglehold on the British economy. Business and the country need Westminster to rule out no deal, and deliver an urgent resolution to the Brexit mess."
That's after Jeremy Corbyn said the discussions had "gone as far as they can", blaming what he called the government's "increasing weakness and instability".
Theresa May said the lack of a "common position" over a further referendum in Labour had made talks "difficult".