Tariffs of 10 percent under World Trade Organization rules would add an average of 3,000 euros to the cost of British-built cars sold in the EU if fully passed on to buyers, and 1,700 euros to the cost of a European auto imported into Britain, the SMMT said.
Any later, and there would be a risk of failing to get it ratified by both parliaments before Brexit Day on March 29.
"I believe that I have put forward serious and workable proposals", May told the summit, according to a senior British government source.
If no deal can be found with the European Union, and with Theresa May having already promised Parliament a meaningful say on the final deal, the scenario is now looking extremely likely to cause an unprecedented constitutional crisis.
Shadow Brexit secretary Sir Keir Starmer said: "It has been clear for weeks that Theresa May's Chequers proposals can not deliver the comprehensive plan we need to protect jobs, the economy and avoid a hard border in Northern Ireland".
Jean-Claude Juncker, who heads the EU Commission, is one of the leaders whom May failed to impress.More news: Meghan Markle Brings Her Mom Along For Her First Royal Hosting Event
The other stumbling block remains the "backstop" plan for the Ireland/Northern Ireland border if no trade deal is agreed by the time the United Kingdom leaves the EU. The EU has insisted that the single market can not be cherry-picked like that.
The 67-year-old added that talks were in the "home straight" during a speech in Brussels last night, although two key issues remained unresolved ahead of October's deadlines - one being the problem surrounding the Irish border.
At dinner at the Felsenreitschule theatre - known to film fans for a scene in the musical "The Sound of Music" - May was due to make another pitch for support for her Chequers plan.
May's third choice, which she was already rehearsing in Thursday's awkward press conference, is to brush off the downbeat words of her European Union counterparts in Salzburg as a negotiating tactic - and cling on to Chequers.
Chancellor Angela Merkel agreed, saying the tone of discussions at the Salzburg summit showed the "atmosphere" of Brexit negotiations were improving.
She predicted a Canada-style free trade deal would be proposed, which would mean "red tape", a "blindfold Brexit" or a "no deal Brexit with Britain cut off from trade with Europe". "I am still optimistic".More news: Valencia vs. Juventus - Football Match Report
He added: "The Irish question remains our priority too and for this we need only goodwill - which we feel, the atmosphere was better than two or three weeks ago - but the Irish question needs something more than good intentions". Ireland is a country that obviously wants to avoid a no deal scenario, we want to avoid a no deal Brexit, (but) we are preparing for that, we are hiring extra staff and officials, putting in IT systems, we're ready for that eventuality should it occur.
"What we want to avoid is any new barriers to the movement of goods, any new barriers to trade, any new barriers to the movement of people", Varadkar said.
Tory activists were already intensely sceptical about the Chequers agreement, which they fear will bind Britain too closely to European Union rules and regulations, and risk fuelling a betrayal narrative among Leave voters.
May had gone to Salzburg and pitched Chequers in person to the EU27, hoping for encouraging words for her plan, which seeks to smooth the path for post-Brexit trade with the continent, and keep borders as open as possible, by closely tying British regulations and tariffs to Europe's.More news: Sony Announces the PlayStation Classic