* May meets CEOs in Downing Street on Brexit
* May says seeks smooth, orderly Brexit
* CEO's raised concern over access to labour - source
* Tone said to be positive (Adds second source, details)
By Costas Pitas
LONDON, Oct 9 (Reuters) - Prime Minister Theresa May told business leaders on Monday that they could be certain there would be a two-year transition period after Britain's exit from the European Union, a source told Reuters.
May, who is trying to ease company concerns that Britain could crash out of the EU without a deal, met business chiefs from GlaxoSmithKline, Vodafone and HSBC and other major companies to hear what they want from talks on Britain's post-Brexit relationship with the EU.
Businesses have become alarmed by the slow progress of negotiations and the prospect that Britain could leave the trading bloc without a new trading arrangement in place in 2019.
"From her point of view, the transitional agreement is non-negotiable ... business should think of the two-year period as assured. It will happen," the source said when asked what May had said during discussions on Monday.
A spokeswoman from May's office said she restated her position "that the government's goal is for a smooth, orderly exit in which there is only one set of changes for businesses and people".
Almost all business leaders expressed concern about access to talent after Brexit and several of them told May that the investment cycle means there are decisions coming at the end of 2017 and the start of 2018, the source said.
Last week, two sources told Reuters that Japanese carmaker Toyota intended to build the next version of its Auris car at its British car plant on the assumption that the government secures a transitional Brexit deal in a decision due by the end of the year.
Both May and her finance minister, Philip Hammond, acknowledged during Monday's meeting that businesses needed a better sense of Britain's post-Brexit relationship with the European Union.
"May said business needs clarity," the source said. "The chancellor (finance minister) said clarity is more important than perfection."
A second source familiar with the situation recognised the outlines of the meeting as given by the first source, adding: "It was a pretty positive tone. There was a detailed conversation and they listened."
"Frankly that was better than before," said the second source, who spoke on condition of anonymity.
Business chiefs have previously complained that their voice has been drowned out by disagreement and division in the government, and they have not heard anything to give them the certainty they need to plan and invest in their businesses.
May's office said she stressed the importance of engaging with the business community to work out methods of implementation, and she promised to continue meeting with a wide range of business opinion.
May was joined by Hammond, business minister Greg Clark, minister for exiting the EU David Davis and trade minister Liam Fox at the council.
Companies attending also included Balfour Beatty, WPP, Morgan Stanley, Aston Martin and AB Foods , the government said.
"We welcome the UK Government’s willingness to listen," a Vodafone spokesman said. "This was a useful and constructive meeting, the details of which are confidential."
The meeting came after May's authority was further undermined last week.
She had to fend off a challenge from up to 30 of her lawmakers who had been pushing for her to quit following a disastrous snap election in June which saw the ruling Conservatives lose their parliamentary majority. (Additional reporting by Paul Sandle, William James and Kate Holton; Editing by Guy Faulconbridge and Richard Balmforth)