Speaking after London announced that Prime Minister Theresa May would start the two-year withdrawal process by writing to European Union summit chair Donald Tusk next Wednesday, the source said this did not leave enough time to convene the other 27 leaders on April 6-7, dates that had been pencilled in for a meeting.
The Bill allows the premier to notify Brussels that the United Kingdom is leaving the European Union, with a two-year process of exit negotiations to follow.
Brexit secretary David Davis said that there is a Fixed Term Parliament Act, which the prime minister intends to honor.
The European Commission, whose chief negotiator Michel Barnier will spearhead the talks with London on behalf of the other 27 member states, said it was ready for the Brexit process. However, the prime minister's spokesman was adamant that Downing Street remained opposed to an election before 2020. Next Wednesday, the Government will deliver on that decision and formally start the process by triggering Article 50.
Britain's Parliament last week gave its final approval to May's Brexit plans, and the prime minister had at one point been expected to trigger Article 50 then. But May has so far rejected the call for a new Scottish referendum until after Britain leaves the EU.
Prime Minister Theresa May is desperate to show that the United Kingdom wants to harbour a good relationship with Europe and she is emphasising British co-operation on training, cyber security and maritime patrols.
"We are ready to begin negotiations", he said.
While this is all well and good, the rosy picture for the government painted by these figures assumes that Theresa May actually achieves the sort of Brexit she wants.
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The announcement meets May's longstanding commitment to trigger Article 50 by the end of March 2017.
It will be the first time that the provisions of Article 50 - which sets out the process for any EU member state "to withdraw from the Union in accordance with its own constitutional requirements" - have been activated.
The European Commission is expected to provide an initial answer to Britain's Article 50 notification within 48 hours but negotiations are not expected to start for several weeks or even months.
By 40% to 30% people think this version of Brexit would be bad for the country, and only 29% say they would be happy with the outcome.
Britain's commitment to payments into the European Union budget - which officials in the bloc estimate to reach around 60 billion euros - are shaping up to be one of the first, and possibly most contentious, parts of the divorce talks.
Sturgeon has made plain her view that Britain is heading for a "bad deal" on Brexit and wants Scotland to have a vote on independence before the terms of the deal are signed.
He said that there must be a very clear sequencing.