Video report by ITV News Correspondent Angus Walker
Boris Johnson has written to the EU, saying that the Irish backstop must be dropped if a deal is to take place.
The letter comes just hours after Downing Street said freedom of movement between the UK and the EU will end on Brexit day, if Britain leaves the bloc with no-deal.
However, following conversations between the Prime Minister and the Irish premier, free movement between the UK and Ireland will still continue.
In his letter to EU Council President Donald Tusk outlining his opposition to the Irish backstop element of the Withdrawal Agreement, Mr Johnson said his Government's "highest priority" remains to leave with a deal, but this could not happen if the backstop remained part of the Withdrawal Agreement.
He added: "It is anti-democratic and inconsistent with the sovereignty of the UK as a state.
"The backstop locks the UK, potentially indefinitely, into an international treaty which will bind us into a customs union and which applies large areas of single market legislation in Northern Ireland.
"The treaty provides no sovereign means of exiting unilaterally and affords the people of Northern Ireland no influence over the legislation which applies to them."
Mr Johnson said he is committed to ensuring there is no return to a hard border on the island of Ireland.
He proposed "flexible and creative solutions to the unique circumstances on the island of Ireland".
He added: "I propose that the backstop should be replaced with a commitment to put in place such arrangements as far as possible before the end of the transition period, as part of the future relationship.
"I also recognise that there will need to be a degree of confidence about what would happen if these arrangements were not all fully in place at the end of that period.
"We are ready to look constructively and flexibly at what commitments might help, consistent of course with the principles set out in this letter."
Mr Johnson acknowledged that "time is very short" but said: "The UK is ready to move quickly, and, given the degree of common ground already, I hope that the EU will be ready to do likewise."
ITV News Correspondent Angus Walker says that many of the points made in Boris Johnson's letter have already been made many times before. He adds that many of the Prime Minister's critics say he latest move is just him "trying to get ahead of the blame game".
Downing Street's insistence that freedom of movement will end if the UK leaves the EU without a deal follows reports that officials had warned against an immediate change on Brexit day if this were to happen.
It was previously reported that Theresa May's government was considering extending freedom of movement rights for EU citizens until 2021
But Number 10 said the system allowing European Union citizens to freely live and work in the UK would “look different”, with changes including tougher checks to prevent foreign criminals entering the country.
Ministers were warned that dramatically changing the system on October 31 could leave the UK facing “another Windrush” – a reference to the immigration scandal which led to Amber Rudd’s downfall as home secretary.
Home Office officials produced a discussion paper for a ministerial no-deal Brexit meeting last week warning that doing so could present a “handling and reputational risk” for the Government, the Times reported.
A source told the newspaper the document raised concerns that an “interim” immigration system would prove impossible to enforce because the Government and employers would be unable to distinguish new arrivals from those already here.
It recommended that free movement should continue until the new immigration system was ready in January 2021 to provide “maximum certainty” to EU citizens and employers.
Details of other changes are being developed and will be set out by Prime Minister Boris Johnson and Home Secretary Priti Patel.
The Prime Minister wants an Australian-style points-based immigration system tailored to suit the UK’s needs after Brexit.
A Downing Street spokesperson insisted that EU citizens currently resident in the UK would not be prevented from re-entering the country after trips abroad, although it was unclear how checks would be carried out.
The system allowing EU citizens to apply for settled status would be unchanged and the two million who had not yet completed the process would not be prevented from entering the UK by the ending of free movement, the spokesperson added.
However, on Monday, Mr Johnson and his Irish counterpart clarified the freedom of movement between Ireland and the UK.
The pair spoke by phone for almost an hour and "the Prime Minister made clear that the common travel area, which long predates the UK and Ireland joining the EU, would not be affected by the ending of freedom of movement after Brexit", a Downing Street spokesperson said.
The common travel area is a special travel zone between the Republic of Ireland and the UK, Isle of Man and the Channel Islands, which dates back to the establishment of the Irish Free State in 1922.
The UK and Irish governments have previously expressed their desire to maintain the common travel area after Brexit and EU negotiating guidelines state that they would respect such bilateral agreements.
However, a House of Commons briefing paper from June 2017 quotes constitutional expert Professor Bernard Ryan, of Leicester University, who questioned the extent to which the rights of Irish nationals in the UK are secured by existing law.
Prof Ryan warned new legislation could be required to protect Irish nationals' status in the UK post-Brexit.
It was also announced that Mr Johnson will visit Dublin in early September, and that during their conversation the two leaders also discussed a number of other matters, including the Withdrawal Agreement.