The Clwyd West MP warns that any such deal would be a "betrayal of trust" and risk 'a whirlwind of public anger'.
Brexit Secretary David Davis will tell French President Emmanuel Macron - don't try to stop us leaving the EU.
In the political turmoil following last week's inconclusive General Election, there have been reports that senior ministers including the Chancellor Phillip Hammond are pressing for a new approach to leaving the EU.
But her vulnerability at home means that her plan to leave the EU's lucrative single market and customs union in order to impose strict limits on immigration is under intense scrutiny.
The sensitive issue has been thrown into further doubt by May's efforts to seek a deal with Northern Ireland's ultra-conservative Democratic Unionist Party to stay in power after the British election.
It is also 82 days after Theresa May sent a letter formally notifying the European Council of Britain's intention to withdraw.
He said: "No deal would be a very, very bad outcome for Britain, but there is a possible worse outcome and that is a deal that is deliberately structured to suck the lifeblood out of our economy over a period of time".
A Great Repeal Bill to transfer all European Union laws to British jurisdiction will be unveiled on Wednesday along with measures to control immigration.
Without a majority for her Conservatives in the UK Parliament, May now says she will work to reflect the wide range of views on Europe that exist in Britain, a signal her Brexit policies could soften.
Britain seems to have tacitly accepted the EU's plan for sequenced talks, which will focus first on the terms of Britain's withdrawal, with negotiations on a future relationship and trade deal coming later.
The two chief negotiators, Michel Barnier of the European Union and David Davis from Britain, immediately set off to find common ground in their working relationship, an important touchstone to see how amicable the biggest political divorce in decades will become. "A deal that supports growth will allow companies to hire more people, raise living standards and improve lives across the country".
When they finally gather round the table in Brussels, the two sides will not only have to unpick a relationship dating back more than 40 years, they will also be attempting to negotiate an ambitious free trade agreement.
European Union officials acknowledge that the agreements to be reached before Britain leaves in March 2019 can only be concluded as a whole package simultaneously but leaders have barred Mr Barnier from talking about trade before he gets outline deals on the rights of expatriate citizens and how much Britain owes the EU.
"Our lawyer let me know about the change in the law and, after a year-long process we are now expecting to get all of our original deposit back plus interest".
A spokesman for the Department for Exiting the European said: "We believe that the withdrawal process can not be concluded without the future relationship also being taken into account".
Germany: no punishment for UK, but EU exit good for no one
If so, it could have to be ratified by up to 38 national and regional parliaments, with any of them effectively holding a veto. The EU insists that should wait until an outline agreement on divorce terms, ideally by the end of this year.
Fleury among players exposed for Vegas NHL expansion draft
Cole, 28, has turned into a bedrock defenseman for the Penguins over the last two-plus years since coming over in a trade from St. Building through the draft is the best way to create sustainable success , and McPhee seems committed to that in Vegas.
Koepka runs away from field to collect US Open
Koepka moved to 14-under with a birdie at the par-5 14th hole. "For us it was like two minutes, it wasn't much", Koepka said. Koepka became the sixth consecutive first-time major victor with his sensational performance Erin Hills , Wisconsin.
US Open: Brooks Koepka wins 117th US Open
Opens, on different courses in a different era, told the new victor , "You don't know it, but your life has changed overnight". Koepka also noted that the major title was especially sweet on Father's Day since he didn't get anything for his dad.
ICC Champions Trophy 2017 Final
He was eventually out when he sliced medium-pacer Hardik Pandya and Jadeja, running back from point, held a well-judged catch. Pakistan recovered splendidly from the loss to India in the first league game to win all the remaining matches.
NASCAR Cup Series: Pocono 400 live stream
Fox Sports 1 provides live television coverage starting at 3 p.m. (18) Kyle Busch , Toyota, 179.151 miles per hour . I knew that going into it. "I hope it can start to change some things about the way we're appreciated in the sport.
Juneteeth camp educates, celebrates African-American culture
Just in time for Juneteenth, a rededication ceremony and day-long festival were held on Saturday to honor the park's improvements. Gordon Granger, arrived in Galveston, Texas, that the final battles against the defenders of slavery were won.