Britain will leave the European single market when it quits the European Union, Theresa May has said.
Mrs May said that her plans for Brexit cannot allow continued membership of the single market, which would require free movement of people and accepting the jurisdiction of the European Court of Justice.
Instead, she said that she will seek "the greatest possible access to the single market on a reciprocal basis, through a comprehensive trade agreement".
Mrs May said that she wanted to remain part of a customs agreement with the remaining 27 EU states, but said she had an "open mind" over whether this would be through associate membership of the Customs Union or through some other arrangement.
Her announcement came in a high-profile speech in London setting out her objectives for post-Brexit Britain.
She also revealed that the final Brexit deal reached between the UK and European Union will be put to a vote of both Houses of Parliament in the UK.
Mrs May did not make clear whether a vote against the agreement would result in the UK remaining in the EU or in Britain crashing out of the 28-nation bloc without a deal.
Speaking at Lancaster House, Mrs May said: "When it comes to Parliament, there is one ... way in which I would like to provide certainty. I can confirm today that the Government will put the final deal that is agreed between the UK and the EU to a vote in both Houses of Parliament before it comes into force."
Under Article 50 of the EU treaties, Britain will have two years to negotiate a deal after it informs the European Council of its intention to quit - something which Mrs May has said she will do by the end of March.
Chief EU negotiator Michel Barnier has suggested that an agreement must be concluded by October 2018 to allow time for ratification before Britain leaves in March 2019, meaning that the Commons and Lords votes are likely to come during that six-month period.
Mrs May said that Britain will maintain "practical arrangements on law enforcement and the sharing of intelligence material" with its former EU partners, as well as continuing to work as closely with European allies on foreign and defence policy as it now does with the EU.
Mrs May said the UK would regain control of its borders.
"We will get control of the number of people coming to Britain from the EU. Because, while controlled immigration can bring great benefits, filling skill shortages, delivering public services, making British businesses the world beaters they often are, when the numbers get too high, public support in the system falters."
The British PM said Britain would no longer be under the jurisdiction of the European Court of Justice after Brexit.
And Mrs May stated she would work to maintain the common travel area with the Republic of Ireland.
Mrs May said remaining in the single market would mean "to all intents and purposes" not leaving the EU.
"As a priority we will pursue a bold and ambitious free trade agreement with the EU.
"This agreement should allow for the freest possible trade in goods and services between Britain and the EU’s member states.
"It should give British companies the maximum possible freedom to trade with and operate within European markets and let European businesses do the same in Britain.
"But I want to be clear: what I am proposing cannot mean membership of the single market."
European leaders had stressed that single market membership meant accepting free movement of goods, services and people.
Being out of the EU but remaining in the single market would also mean being bound by the rules and regulations without having a say in how they are drawn up.
"It would, to all intents and purposes mean not leaving the EU at all," she said.
"That is why both sides in the referendum campaign made it clear that a vote to leave the EU would be a vote to leave the single market."
Mrs May said the UK would seek the "greatest possible access" to the single market through a "new, comprehensive, bold and ambitious free trade agreement".
The deal could take in elements of single market arrangements in areas such as the automotive industry or financial services, she said.
"An important part of the new strategic partnership we seek with the EU will be the pursuit of the greatest possible access to the single market on a fully reciprocal basis through a comprehensive free trade agreement," she said.
The Prime Minister added that leaving the single market would mean no longer having to pay "huge sums" to the EU budget - but the UK could continue to pay to participate in some programmes.
Mrs May repeated her desire to reach an early deal on the status of British citizens in the EU and those from the continent living in Britain.
She also vowed to ensure workers’ rights are "fully protected and maintained".