* MPs want more say over final Brexit deal
* Exit day for Britain is March 29 2019
* Amendment relates to EU withdrawal bill (Adds PM May warning, details)
LONDON, Dec 13 (Reuters) - Prime Minister Theresa May warned rebellious lawmakers in her own party they could endanger Britain's smooth exit from the European Union if they tried to change her Brexit blueprint later on Wednesday.
May has tried to avert a rebellion in parliament by promising parliament a series of votes on any deal to leave the EU "as soon as possible" after Brexit talks end, but offered little new ahead of Wednesday's session.
Members of Parliament (MPs) are debating new laws which will repeal the 1972 legislation binding Britain to the EU and copy existing EU law into domestic law to ensure legal continuity after 'Exit Day' on March 29, 2019.
After six days of debate in parliament ranging from the legal minutiae of Brexit to the gaping differences between 'Remainers' and 'Leavers', May could face a defeat as lawmakers demand more say over the final exit deal.
Wednesday's likely flashpoint is an amendment put forward by a member of May's own party, the government's former attorney general, Dominic Grieve, who wants parliament to have a meaningful vote on any deal before it is finalized.
But May warned that his proposal could push the complex task of transposing EU law legislation right to the end of the two-year negotiation period triggered earlier this year.
"That could be at a very late stage in the proceedings which could mean that we are not able to have the orderly and smooth exit from the European Union that we wish to have," she told parliament before an hours-long debate on the exit plan.
If passed by a simple majority vote, the amendment would require parliament to approve the government's final Brexit deal by passing a separate written law once the terms of the withdrawal agreement are known.
That could allow lawmakers to send May back to the negotiating table if they do not like the deal -- something that might not be supported by EU negotiators.
Earlier on Wednesday, the European Parliament urged EU leaders to allow the next phase of talks to start, backing a motion that recognized they had advanced sufficiently as well as a line criticizing Britain's negotiator David Davis.
The government has conceded that a separate piece of legislation, allowing members of parliament more say on the deal, will be needed and aims to pass another bill implementing the Brexit agreement once final terms are agreed with Brussels.
But Grieve signaled that might not go far enough for him to withdraw the amendment he says is needed to ensure parliament is allowed to play its role of holding government to account.
"My impression of the last few days, when I've been talking to the government, is it seems to be a bit of a dialog of the deaf. They've sort of turned this into a battle of wills," he told Sky News.
"This is a completely pointless exercise. They need to listen to the point that's being made and they need to respond to it."
May is in a precarious position. In June, she gambled on a snap election to strengthen her party's majority in the 650-seat parliament but instead bungled her campaign and ended up with a minority government propped up by the 10 votes of a small, pro-Brexit Northern Irish party.
Since then she has struggled to assert her authority over a Conservative Party which is deeply divided over the best route out of the EU.
The government has been forced to give ground on several issues to ward off other rebellions over the Brexit laws.
But after striking a deal with Brussels last week to move exit negotiations on to the next phase, covering trade and transition arrangements, May won approval from both the Remain and Leave factions of her party, suggesting attempts to unseat her were on hold.
(Additional reporting by Kate Holton; Editing by Catherine Evans)