The Queen's Speech will not take place on 14 October as originally planned unless there is a decision to prorogue Parliament, Downing Street said.
The Supreme Court ruled that Parliament was not prorogued and a Queen's Speech cannot take place without prorogation.
A Number 10 spokesman said the Government is "looking at the precise implications" of the Supreme Court judgement.
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The Government had insisted that prorogation was necessary to start afresh with new legislation from what is effectively a brand-new administration.
Prime Minister Boris Johnson wanted to bring forward an "ambitious domestic agenda" that he believed required a Queen's Speech.
The session had originally come to an end in the early hours of Tuesday 10 September when Parliament was thought to have been prorogued - or suspended - until 14 October.
But as the Supreme Court ruled the prorogation unlawful, it means the session did not technically end at all.
Asked if the Queen's Speech will still take place on 14 October, a spokesman for the Prime Minister said: "Because Parliament was not prorogued as a result of the Supreme Court's ruling, you can't have a Queen's Speech without a prorogation, so that date has in effect fallen away."
He added: "That date, as was originally set out, required prorogation to take place. The Supreme Court's judgement was that Parliament hadn't been prorogued so therefore it drops away."
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The spokesman added: "It could only happen in the event that a decision was taken to prorogue Parliament and that's not where we are currently."
It is understood the Government is looking at whether or not there will be a prorogation and then a date for a Queen's Speech would be decided at that point.