* PM May worries executives with transition deal comments
* Some say transition terms needed by first quarter of 2018
* Companies becoming more vocal about need for early deal
LONDON, Oct 24 (Reuters) - Executives at some of Britain's largest companies have reacted with alarm to Prime Minister Theresa May's statement that the details of any transitional arrangements with the European Union may not be known until a broader trade deal has been agreed.
Already rattled by the slow progress of Brexit talks, businesses operating in the world's fifth largest economy have been pressing for months for details about what any transitional EU trade deal will actually look like.
May had promised to retain full access to the EU's single market for two years after Brexit and told executives from leading British companies two weeks ago they should consider a transition period as assured.
But the prime minister surprised many on Monday when she told parliament that any transition deal would be part of a wider trade agreement - meaning companies may not have specific details about interim trade arrangements for some time.
Britain is due to leave the EU in March 2019 and many companies say they need to know the terms of any transition deal at least a year beforehand to reap any benefits while some banks have already triggered contingency plans.
"The difficulty is timing," Barclays Plc Chairman John McFarlane told Reuters. "We can avoid material dislocation if we know by the end of the first quarter next year, although real money is likely to be spent if uncertainty persists."
McFarlane said he believed Brussels was open to a transition deal that gave businesses and the British government time to adjust to the post-Brexit world, but an agreement needed to be reached as soon as possible.
A spokesman for May tried to provide more clarity on Tuesday saying Britain hoped to agree a broad framework for its transitional trade agreement quickly, but declined to say when such a deal might be reached.
"It is incredibly disheartening," said Catherine McGuinness, the political leader of the City of London's municipal body. "Clarification around a transition so late in the day will be like closing the stable doors once the horse has bolted."
Reuters spoke to seven senior executives at leading companies in Britain on Tuesday as well as five business organisations to get their reaction to May's comments.
Concern about Brexit arrangements had been growing even before May's comments on Monday spooked executives further. The country's five leading business organisations warned on Monday that companies would start moving jobs and investment out of Britain if they do not get a transition deal soon.
An executive at a company in the FTSE 100 index of blue-chips said its management had spent much of Tuesday morning trying to establish if May had misspoken in parliament, or whether her statements had been incorrectly reported.
"I can understand it politically and from a negotiation point of view, but from a business point of view, this is going to cause problems," the executive, who declined to be named, said.
Executives at some other FTSE 100 companies were also confused by May's statement on Monday, saying it was the latest example of a lack of coherence from the government about its Brexit plans, and that they needed hard details.
Several opposition lawmakers pressed the prime minister in parliament on Monday to clarify what her negotiating stance meant for businesses.
"The issue of an implementation period is about practical arrangements to reach the future partnership, and you do not know what those practical arrangements are until you know what that future partnership is," May told lawmakers.
Companies have become increasingly vocal in recent weeks about fears that Britain could crash out of the world's biggest trading bloc without any deal.
Some businesses, including the biggest banks and financial institutions, have already identified locations in Europe to open offices and reallocate staff because of a lack of clarity.
An executive at a U.S. bank in London said at this point words would no longer suffice to reassure businesses that a transition deal would fall into place.
"When you sit down with your lawyers they will warn business that soft sounding words are not enough," he said.
British officials say they can agree a trade deal with the EU next year but EU Brexit negotiator Michel Barnier said in comments published on Tuesday it would take until the end of 2020.
"May consistently says a transition ... period will be agreed because she truly believes she will have an agreement on a future trade deal by March 2019," said another banker at a major international lender. "She is the only person in the entire world who believes that is possible." (Additional reporting by Kate Holton and William James; editing by David Clarke)