"Together we represent millions of workers and tens of thousands of businesses. It is on their behalf that we are writing to you to ask you to change your Brexit approach," the letter said in its opening paragraph.
The letter, signed by TUC General Secretary Frances O'Grady and CBI Director-General Carolyn Fairbairn, said that UK companies and communities were not ready for the risks of a no-deal Brexit.
"We ask you to take three steps to protect the jobs, rights and livelihoods of ordinary working people. First, avoiding no deal is paramount… Second, securing an extension has become essential… Third, 'the current deal or no deal' must not be the only choice. A Plan B must be found — one that protects workers, the economy and an open Irish border," the letter read further.
The letter's authors also requested an urgent meeting with May.
The UK government has been in a state of crisis as the Brexit deadline is looming. If the UK parliament does not reach an agreement on an exit deal and a Brexit extension is not granted, both the United Kingdom and the European Union will face economic uncertainties in a "hard exit" scenario.