All trade in goods between EU member states must be free of customs duties
The PM has repeatedly stated the UK will leave the customs union, but pressure from Labour and some in her own party has prompted fears among ardent Leavers that a compromise could be reached. But what does it all mean?
:: What is a customs union?
A customs union is defined as a group of states that have agreed to eliminate customs duties (import taxes) on trade between themselves, as well as reduce other administrative requirements.
It also sees those states impose a common external tariff on imports from non-members.
:: What is the EU's customs union?
The EU's customs union means all trade in goods between member states must be free of customs duties.
All members must also impose the bloc's common external tariff on all goods arriving from outside the EU.
This means once imported into the EU, goods can then move around the bloc without any further customs checks.
:: So, will Britain be leaving the EU's customs union?
Yes, most probably. Membership of the EU's customs union is written into the bloc's treaties, which will cease to apply to the UK in March 2019.
Labour's shadow Brexit secretary Sir Keir Starmer has stated the "customs arrangements at the moment are hardwired into the membership treaty".
Tory MP Anna Soubry has tabled a cross-party amendment to the Trade Bill in an attempt to force the Government to retain a customs union with the EU. Tory rebels and Labour Remainers could force this amendment through Parliament.
Although Monaco and the British territories of Akrotiri and Dhekelia, Guernsey, the Isle of Man and Jersey are not EU members, they are part of the EU's customs arrangements through their relationship with full member states.
:: But, Britain could form a new customs union with the EU, right?
Again, yes. Non-EU countries such as Turkey, Andorra and San Marino are each in a bilateral customs union with the EU.
Labour now wants the UK to enter such a customs union with the EU after Brexit through a new treaty that will "do the work of the current customs union".
The Government has ruled out any form of customs union with the EU once Britain leaves the bloc.
However, the PM is struggling to reconcile the demands of warring Brexiteers and Remainers and does not need any more Cabinet resignations.
She also faces near-civil war on her backbenches, with pro-Remain Tory rebels threatening to vote with Labour and other opposition parties in the Commons to stay in the customs union.
:: Does remaining in any form of union stop the UK signing free-trade deals with non-EU countries?
This is debated among politicians and would likely depend on the nature of any customs union negotiated between the EU and the UK.
As a current member of the EU's customs union, trade deals with non-EU countries are negotiated on the UK's behalf by Brussels.
One of the main benefits of Brexit touted by Leave supporters is that it will allow Britain to regain control over its own trade policy and sign deals with countries such as the US, China and Australia.
They say it will also allow the UK to reduce tariffs on imports, such as produce from the developing world, thereby boosting those countries' economies and meaning cheaper prices for British consumers.
Brexiteers argue re-entering a new customs union with the EU after Brexit will hinder those ambitions.
Even arch-Remainer Tony Blair has dismissed the prospect of Britain having an effective, independent trade policy if it remains in a customs union with the EU.
But Labour says the UK would be "more likely" to sign new trade deals after Brexit by doing it "jointly" with the EU through a customs union with the bloc.
:: But, can't Turkey sign its own trade deals?
Remain-supporting Tory MP Nicky Morgan has insisted it is "perfectly possible" for Britain to remain in a customs union with the EU.
She has cited Turkey's ability to sign its own trade agreements in sectors which are not covered by its customs union with the EU, such as agriculture.
But critics say this is merely theoretical and, in practice, proves too complicated for Turkey to do.
They also point to how Turkey has to open its markets to any new country the EU strikes a trade deal with, even though it doesn't have any say over how that agreement was negotiated.
Turkey's customs union with the EU was also seen as the first step towards full EU membership for the country.
:: And what does it all mean for Northern Ireland?
It is argued that retaining a customs union with the EU after Brexit is the only way to avoid a hard border between Northern Ireland and the Republic of Ireland, an EU member state.
This is something the UK Government, the Irish Government and the EU are all committed too.
The UK Government has stated options such as customs exemptions for smaller traders, a "trusted trader" scheme for larger businesses and "technology-based solutions" could all be among answers to the Irish border dilemma.
