* May wants two-year transition after UK exits bloc in March 2019
* UK wants outline on transition agreed by next March, says Davis
* Earlier statement by May had unnerved corporate executives
* Britain and EU at odds on overall timeline of negotiations (Adds Brexit department clarification on timing of vote)
LONDON, Oct 25 (Reuters) - Britain wants an outline agreement with the European Union by the end of March 2018 on the transitional arrangements that will apply temporarily after it leaves the bloc, Brexit minister David Davis said on Wednesday.
Davis was addressing confusion caused by Prime Minister Theresa May this week over the exit timetable, but he then stumbled into a new row about when lawmakers would get to vote on a final deal. His department later issued a clarification.
May is seeking a so-called implementation period of around two years after Britain's exit from the EU in March 2019, during which its access to the EU single market would stay largely unchanged while new arrangements are put in place.
"I would be aiming to get certainly the outlines of it agreed, if we could, in the first quarter (of 2018) ... but it's a negotiation," Davis told a parliamentary committee.
Earlier this week May unnerved corporate executives, keen to know the trading rules they will face, by saying any transitional deal would not be agreed until the entire exit agreement was sealed, more likely towards the end of 2018.
Last week EU leaders said at a summit that they would begin preparations to move into "phase two" of the Brexit negotiations in December, a step forward that would allow London to discuss its future trade relationship with the bloc.
Davis said he expected to receive guidance from the EU on its approach to a transitional period by December, and that a deal allowing Britain to maintain conditions similar to the status quo would be struck quickly afterwards.
However, having reassured businesses on the trade deal, Davis then angered lawmakers by suggesting the EU would push negotiations right up to the end of March 2019, meaning parliament might have to vote to approve the exit deal after Britain had already departed the bloc.
Political opponents accused the government of trying to subvert democracy by not giving parliament a proper say.
A spokeswoman for Davis' department later issued a clarification, saying the government was working to get the final deal agreed by October 2018 and that it intended to give lawmakers a vote before Britain left.
"This morning the Secretary of State (Davis) was asked about hypothetical scenarios. (Chief EU negotiator) Michel Barnier has said he hopes to get the deal agreed by October 2018 and that is our aim as well," the spokeswoman said.
May is already facing a rough ride in parliament on her minority government's key piece of Brexit legislation, which is on hold while ministers plough through hundreds of proposed amendments - some of which have enough support to inflict an embarrassing defeat.
"This U-turn exposes another self-created shambles in government over Brexit," Pat McFadden, an opposition lawmaker, said in a statement issued by the pro-European campaign group Open Britain.
TRADE DEAL DIFFERENCES
Despite Davis's comments on the transition deal, Britain and the EU remain at odds on the overall timeline of the negotiations, which incorporate a withdrawal deal on the terms of the divorce, the transitional deal, and a future trade deal.
Britain wants to finish everything by the time it leaves in early 2019, while the EU thinks it could take until 2020 to tie up trade terms.
Davis said he believed Britain would be able to seal a trade and customs arrangement by the end of the two-year exit process, adding that it was important to do so to avoid getting trapped in a protracted negotiation.
"It's not a good position to get into to be still negotiating during such an arrangement," Davis said. "If we were doing the negotiation during a period of transition, I suspect what we would get offered is a year extension and another year extension, each time paying a fee."
An EU official said on Tuesday that the EU will only negotiate on the details of a free trade deal after Britain has actually left in March 2019 because the EU's own laws do not allow it to negotiate trade agreements with its own members.
Asked about this approach, Davis said a trade deal could be signed "a nanosecond" after Britain leaves, implying that he hoped for a more flexible approach from Brussels. (Additional reporting by Estelle Shirbon and Alistair Smout; Editing by Richard Balmforth)