A draft position of the remaining 27 EU members said the bloc was determined to foster a close partnership with Britain, but its depth would be limited by Britain's own wish to leave the EU's single market and customs union.
Varadkar said the European Single Market must be protected throughout the negotiations, adding that he wants "the transition period to be smooth".
Mr Bettel, who will meet the British Prime Minister in London next week, said he "didn't learn that much more than I knew before" from her Mansion House speech.
"Divergence in external tariffs and internal rules as well as absence of common institutions and a shared legal system, necessitates checks and controls to uphold the integrity of the European Union single market as well as of the United Kingdom market".
But the text said in the future, Britain's financial firms would only be allowed to operate in the EU "under host state rules" and be treated according to 'the fact that the United Kingdom will become a third country and the Union and the United Kingdom will no longer share a common regulatory, supervisory, enforcement and judiciary framework'.
"If in London someone assumes that the negotiations will deal with other issues first, before moving to the Irish issue, my response would be: "Ireland first".More news: Lovren preparing for Lukaku battle and 'ugly' Manchester United
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Here the Prime Minister has softened her tone somewhat, recognising that the United Kingdom will continue to be affected by decisions of the European Court of Justice even after the United Kingdom leaves its jurisdiction.
May also says that where the United Kingdom continues to participate in an European Union agency it will have to respect the remit of the ECJ over that agency.
The British Ports Association (BPA) has written to the EU to warn that a free trade agreement on goods could still lead to major disruption and European ports.
He said unlike with the trade of goods, services are about ensuring common rules, common supervision and common enforcement and that is why free trade agreements do not have detailed rules for financial services.
'This means double regulation.
Financial services generate more than 10 percent of Britain's output and are the only area in which Britain has a trade surplus with the European Union, making London very keen to preserve its banks' current access to continental Europe. Although May's speech provided some much needed clarity on key negotiation issues for the United Kingdom, businesses will remain particularly concerned that the detail of the future trade and customs arrangements still remains rather unclear. "What I've said is that the EU's model of equivalence, which is unilateral and withdrawable on no notice in some cases. would not work", Hammond said.