But what happens if no extension is agreed?
What is a no-deal Brexit?
A no-deal break means Britain would immediately cease to be an EU member state and the 585-page Withdrawal Agreement would not apply.
That would mean the planned transition period to the end of 2020 – intended to allow firms to carry on trading with the EU under the existing rules while they adapt to the new arrangements – would not kick in.
It would also affect citizens’ rights, the Irish border and UK’s £39 billion “divorce” bill.
So what would that mean for trade?
The legal basis for the free movement of goods between Britain and the EU would disappear, and instead the UK would move to trading under World Trade Organisation (WTO) rules.
That means a new tariff regime as well as new customs and regulatory checks.
The Government has announced that, as a temporary measure, there would be no tariffs on most goods coming into UK (87% by value compared with 80% at present) although there will be protections for some industries, including meat and dairy producers, car manufacturers and makers of ceramics.
For trade with non-EU countries, the Government has said it wants to carry on with the same arrangements with those countries that have trade deals with the EU.
So far it has managed to “roll over” a number of agreements, including those with Switzerland, Norway and Israel, but others, including those with Japan and Turkey, have yet to be agreed.
How will that work at the border?
Until it actually happens, no-one can be quite sure. The Government has said it will do what it can to ensure that goods continue to flow into the country as smoothly as possible, waiving checks where it can.
However there are concerns that many firms – particularly smaller traders – are still not properly prepared for dealing with the new procedures. That has raised fears of long tailbacks of lorries at the Channel ports, at least in the short term.
There will be new checks on livestock and food products being exported from the UK into the EU as Britain may no longer be considered compliant with EU regulatory standards.
What will be the effect in the shops?
With around 30% of the UK’s food imported from the EU, supermarkets have warned of higher prices and empty shelves in the event of no-deal.
Bank of England Governor Mark Carney has said there could be a hike of 5% to 10% in food prices, while there are concerns about the impact on the supply of perishable goods if no-deal results in delays at the border.
Tariffs could add around £1,500 to the price of a typical car imported from the EU.
Brexiteers, however, argue that many of the concerns are exaggerated, with the UK importing a wide variety of fresh produce from non-EU countries.
What about medicines?
The NHS imports large quantities of drugs and medical equipment from the EU and there are concerns about the impact of no-deal on costs and on complex supply chains.
The Government – which has been urging pharmaceutical companies to stockpile six weeks worth of essential medicines – has said measures are in place to ensure that patients will continue to get the drugs they need.
Extra shipping capacity has been secured and warehouses with refrigeration facilities rented to store medicines, while arrangements have been made to fly in any that cannot be stockpiled.
However there have been reports that some hospitals are already experiencing shortages of drugs as the date for the UK’s departure approaches.
What about citizens’ rights?
No-deal means that there is no agreement on the rights of EU citizens living in the UK and British nationals in the EU.
The Government has said it will continue to guarantee the rights of the estimated three million EU citizens in the UK, allowing them to gain “settled status”, as would be the case if there was a deal.
However Parliament’s Human Rights Committee has warned that Government legislation means they could be denied access to benefits such as council housing and social security payments, even if there is a deal.
For the one million UK nationals in the EU, in the event of no-deal their future status will depend on the individual member states where they are resident.
The European Commission has urged them to adopt a generous approach, but it remains unclear how they will respond.
How will the Irish border work?
Both sides have said there will be no return of physical checks on the border between Northern Ireland and the Republic, but have yet to spell out how it will work in practice.
The UK has said that, as a temporary measure, it will not impose any new checks or require customs declarations on most goods crossing the border into Northern Ireland, while a longer term solution is found.
Irish premier Leo Varadkar has also stated his commitment to an open border.
At the same time, he has assured fellow EU leaders that he will not allow Ireland to become a “backdoor” into the EU single market for goods coming via Northern Ireland, but has not so far explained how that can be achieved.