BRUSSELS (Reuters) - Theresa May s  constructive spirit  won a cautious welcome from the European Union on Friday, though the British prime minister s keynote Brexit speech raised more questions than answers for some and they want more details next week.  The speech shows a willingness to move forward, as time is of the essence,  the EU s chief Brexit negotiator Michel Barnier said in a lengthy statement, adding that May s specially staged event in Renaissance Florence chimed with the spirit of Europe. Echoing reactions from diplomats and officials involved in the negotiations who spoke privately to Reuters, Barnier said it was a  step forward  that May said British courts would protect EU citizens in Britain based directly on a new EU-UK treaty, not on British law, and would take future EU case law into account. But as with vaguer comments about the EU budget, in which May said the other 27 countries would not be left out of pocket over the EU financial cycle ending in December 2020, Barnier stressed that he wants to hear a  precise negotiating position  when he meets his British counterpart on Monday. Similarly, he repeated the EU position on refusing talks on what happens after Brexit in March 2019 until Britain makes  significant progress  in agreeing its divorce terms.  May for the first time spelled out her request for a transition period of about two years after Brexit, during which Britain would stay in the EU s single market. Barnier reiterated that the other 27 could consider the request but again insisted that Britain could not keep all the benefits of EU membership while relinquishing obligations. May s allies in Brussels talked up the significance of a speech she chose to deliver in Florence to drive home a message of future cooperation with Britain s European neighbours.  We can only hope that the EU takes what the prime minister has said seriously, and sees that it is time to move forward,  said the pro-Brexit leader of her Conservative Party s group in the European Parliament, Syed Kamall.  I hope that the clarity provided today will allow for real progress at the next round of negotiations.  However, comments by the German leader of the centre-right group in the EU legislature, an ally of Chancellor Angela Merkel, demonstrated the scepticism felt toward Britain by some of Europe s main powers:  In substance, May is bringing no more clarity to London s positions. I am even more concerned now.  Guy Verhofstadt, the Brexit coordinator for the European Parliament which must ratify any treaty, called May s speech  more realistic  but warned against  cherry picking  EU favours during the transition. His demand that Britain forgo controls on EU immigration during any transition and go on making budget payments beyond 2020 will jar with May s pro-Brexit supporters. Nonetheless, one senior official handling Brexit for an EU government said two phrases from May on expatriates  rights and Britain s financial obligations marked  a real step forward .   That is quite something,  the official said.  Let s see what that means in the concrete negotiations.  Those two elements are among three in which progress toward a deal is a criterion for EU leaders to approve the opening of talks on future trade terms. The third, the new EU-UK land border on Ireland, remains a conundrum and May said nothing new. Another senior official handling Brexit for a big member state said May s speech should help create a  more positive atmosphere  in the negotiations, when Brexit Secretary David Davis arrives in Brussels on Monday for a new week of talks. May will meet the other 27 leaders in Estonia on Thursday and Friday and hopes they could authorise Barnier to launch trade talks as early as an Oct. 19-20 summit in Brussels.  The real problematic issue that remains to be resolved is the financial settlement,  said Konrad Szymanski, the EU affairs minister of Poland, a major beneficiary of EU subsidies that could be hard hit by the loss of Britain s annual contributions. May said other states should not  pay more or receive less over the remainder of the current budget plan . Barnier said he was  ready to discuss the concrete implications of this pledge .  The European Commission has estimated that Britain might owe something like 60 billion euros ($70 billion) on leaving in March 2019. About a third of that, EU officials say, would be down to making Britain pay its roughly 10-billion-euro annual contribution for the remaining two years   2019 and 2020   of the EU s current, seven-year budget programme. However, were Britain to remain in the single market, which would entail payments into EU programmes, that money   some 20 billion euros   would no longer come under the  divorce bill .  Britain has argued that it will owe very little on leaving, countering EU demands that it go on paying for many years after Brexit to cover much longer-term commitments previously made. An EU official told Reuters:  What May said goes further than what the British government has said so far. But ... it is not clear until when they would be willing to pay.  