Britain’s Prime Minister Theresa May speaks in Parliament as she announces that she has sent the letter to trigger the process of leaving the European Union in London, March 29, 2017. (Reuters)

Prime Minister Theresa May is off to a tough start in her quest to pull Britain out of the European Union.

Ms. May formally triggered the EU exit mechanism on Wednesday, beginning a two-year period for the EU and Britain to negotiate the country’s withdrawal. But she’s already faced some notable setbacks.

EU leaders have shot down one of her key priorities and she is facing accusations of blackmail after suggesting that European security will be weakened if the EU doesn’t reach a trade deal with Britain.

In her six-page letter sent Wednesday to Donald Tusk, the head of the European Council which represents EU leaders, which triggered Britain’s departure, Ms. May indicated that she wanted to use the two-year time frame to negotiate the terms of separation as well as a free-trade deal. That has been a key proposal for Ms. May for months, and she has insisted that Britain and the EU can work out a comprehensive trade agreement in parallel with the exit talks.

On Thursday, French President Francois Hollande joined German Chancellor Angela Merkel in rejecting the idea.

During a phone call with Ms. May, Mr. Hollande “indicated that the talks must at first be about the terms of withdrawal, dealing especially with citizens’ rights and obligations resulting from the commitments made by the United Kingdom,” according to a statement from the French government. “On the basis of the progress made, we could open discussions on the framework of future relations between the United Kingdom and the European Union.”

That echoed comments from Ms. Merkel on Wednesday and it leaves Ms. May forced to rethink her government’s strategy. Separating the two discussions could add considerable time to the overall process since negotiating a trade deal can take years. The EU is also keen to resolve Britain’s payment for assorted obligations, which could total £50-billion ($71-billion Canadian), before launching into trade talks. Ms. May has rejected that figure but has conceded that some amount might have to be paid.

David Davis, the British minister in charge of Brexit, said that Britain will continue to press the issue. “There is an area of argument over this. Which is fine. And that will go on,” he told the BBC on Thursday. “The reason we want to see it done in parallel is we think the best way to get a deal is to look at the whole package together.”

Ms. May’s comments linking security with a trade deal have also sparked sharp comments from EU officials. In her letter to Mr. Tusk, Ms. May mentioned security issues 11 times and added: “In security terms a failure to reach agreement would mean our co-operation in the fight against crime and terrorism would be weakened.” That was seen as a threat by some EU officials.

“What I think is not possible is to say to the European Union, ‘Well, look we will only co-operate on security if you give us a good trade deal or a good economic package,’ that is not done,” Guy Verhofstadt, the chief Brexit negotiator for the European Parliament, said Thursday. “The security of the citizens is so important, the fight against terrorism is so crucial, that you cannot negotiate with something else. What we propose is to make an association agreement between the U.K. and the EU with two consistent pillars, one on security, the fight against terrorism, external and internal; and at the other hand a good trade deal, a fair trade deal, where it is clear, naturally, that outside the European Union, you can never have a status that is [as favourable as EU membership].”

Mr. Davis played down the Prime Minister’s comments, saying there was no attempt to blackmail the EU. “We want a deal. That’s the point. We want a deal,” he told the BBC. “And [Ms. May] was making the point that it is bad for both of us if we don’t have a deal. That, I think, is a perfectly reasonable point to make and not in any sense a threat.”

On Thursday, the British parliament also began the lengthy process of uncoupling the country from more than 40 years of EU laws and regulation. Mr. Davis introduced a plan to incorporate an estimated 19,000 EU laws and regulations into the British statute books. Members of Parliament will then have to spend years deciding which to keep, which to amend and which to scrap. The plan also calls for Parliament to officially repeal the legislation that brought Britain into the forerunner of the EU in 1973.