LONDON (Reuters) - British Prime Minister Theresa May told parliament her plan on Monday for a Brexit transition period with broadly the same access to European Union markets but was met with scepticism from pro-Brexit lawmakers fearful of a watered-down EU exit.

May secured an agreement with EU leaders last week to move previously-deadlocked talks forward onto the topic of interim and long-term trading arrangements.

On Monday, she reported back to parliament on those talks, setting out the framework of a roughly two-year implementation period designed to smooth Britain’s EU exit and provide clarity for businesses and citizens.

“This will help give certainty to employers and families that we are going to deliver a smooth Brexit,” May said. She added that negotiating guidelines agreed last week point to a shared desire with the EU to make “rapid progress” on a deal.

The outline of the transition period that May presented is consistent with plans she has previously set out and largely in line with what Brussels wants, but remains subject to negotiation.

“During this strictly time-limited implementation period which we will now begin to negotiate, we would not be in the single market or the customs union, as we will have left the European Union,” May said.

“But we would propose that our access to one another’s markets would continue as now, while we prepare and implement the new processes and new systems that will underpin our future partnership.”

May said during the interim period, Britain wants to begin registering the arrival of EU citizens in the country in preparation for a new immigration system, and would hope to agree, and even sign, trade deals with non-EU states.

“VASSAL STATE”

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But the plan was not universally accepted by lawmakers in May’s Conservative Party, which is deeply divided over the best route out of the bloc.

Jacob Rees-Mogg, one of several pro-Brexit Conservatives to express concern, called on May to reject the EU’s negotiating guidelines because they would make Britain “no more than a vassal state, a colony, a serf of the European Union.”

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May is reliant on the backing of all members of her party to put her Brexit plans into action, having lost her parliamentary majority in an ill-judged snap election earlier this year which left her needing the support of a small Northern Irish party.

Last week May’s fragility was exposed by the rebellion of 11 largely pro-European Conservative lawmakers in a parliamentary vote on Brexit legislation that led to an embarrassing defeat. The rebels have since drawn harsh criticism from some party members, and received threats of violence online.

“We are dealing with questions of great significance to our country’s future, so it is natural that there are many strongly held views on all sides of this chamber,” May said.

“But there can never be a place for the threats of violence and intimidation against some members that we have seen in recent days.”

Earlier on Monday, May met key ministers to discuss the even thornier issue of what the country’s long-term relationship with the EU should be - the first time since the June 2016 vote to leave that she has broached the topic with cabinet members.

A full cabinet discussion on the so-called “end state” of the Brexit talks is then due on Tuesday.