A huge 62 per cent are dissatisfied in the PM.
The only solace for Mrs May is Labour leader Jeremy Corbyn also being blighted by bad ratings.
The survey showed even more dramatic drop in the rating of may the members of her Conservative party - from 68 to 55%.
Increasing discussion about the prospects of a no deal Brexit and risks of food and medical shortages may have fuelled support for the idea.
As before the referendum, when President of the European Council Donald Tusk warned Brits that voting to Leave could mean "the end of Western political civilisation" and David Cameron asked then-U.S. President Barack Obama to threaten to send the country to the "back of the queue" for a trade deal, former Remain campaigner Theresa May appears to have support from overseas for her scare tactics.More news: Harley Davidson Announces Huge Plans for India; 250-500 CC Bikes Arriving
Public support for a new referendum is split along Leave/Remain lines, with just 19% of Leavers backing a new poll, compared with 66% of those who voted to Remain.
The Sky poll said 65 percent of British voters thought the government would end up with a bad deal - an increase of 15 points from March - and half support a referendum to choose between leaving with a deal, leaving without a deal or staying in the EU.
When asked to choose between three options - May's deal, a no deal or staying in the European Union - 48 percent said they would prefer to stay in the European Union, 27 percent wanted to leave with no deal and 13 percent would opt for the government's deal.
Furious Footy Brexiteers responded to the star with their opinions calling him a "disgrace" and said he should "stick to football". They don't want a shoddy deal full of second-rate concessions, or a nightmare no deal.
Labour MP Caroline Flint also warned those fighting for a so-called "People's Vote" could vote "more emphatically" to leave if there was another Brexit referendum.