May stated that Britain wants to keep the same economic relationship with the EU as before for two years after leaving the bloc.
But what happens after that?
"On the one hand those who want a relatively hard Brexit are willing to accept that we do have our obligations including to the existing EU budgetary cycle and their concern will be 'OK, but at the end of those two years we'll still be looking for a relationship in which we are not part of the single market'," says John Curtice, Professor of Politics at Strathclyde University in Scotland.
"For others, however, one of the points about a transition period is that perhaps as a result of this it might be possible to get the time to engineer a trade agreement with the European Union which almost implies being in the single market."
Brussels has said clearly that Britain can keep close economic ties with the EU after Brexit but only if it accepts EU rules. However, it seems that many in the UK government share Foreign Secretary Boris Johnson's position that "we can have our cake and eat it".
"I think the [EU 27] are completely baffled, because they are trying to negotiate with a country that has not reached an agreement with itself about what it wants," says Quentin Peel, expert on European politics at Chatham House in London.
"As a result, the negotiations go nowhere. Let me give you an example - a good example of the sort of deal that might be possible and the problem - and that is a deal to keep the City of London as the most important financial centre for the whole of Europe."
A senior German official told him last week they would be "delighted to keep the City of London as the real focus" but on condiution of that all parties agree on the common rules.
"And that's where it hits a brick wall on the British side, because the British say 'No no no, we want to have the right to set our own rules for the City of London - regardless of what the EU may demand'."
Difficulties over Northern Irish border
As well as those economic matters, the Northern Irish border is another difficult Brexit issue.
The EU says there must be progress on this issue before talks can start on the UK's future economic relationship with it. Meanwhile, the British government says it wants to leave the single market and customs union while keeping the Irish border open.
These UK positions seem contradictory.
"The only way it could remain open would be if Northern Ireland and the Republic of Ireland were effectively in some sort of common economic zone, which would make Northern Ireland quite clearly separate from the rest of the United Kingdom," says Peel.
"That's something that the unionists [who want Northern Ireland to stay in the UK], who are supporting Theresa May's government in the House of Commons and without whom she has no majority, they are adamant that they will not accept any deal that makes Northern Ireland in any way separate from the United Kingdom. So I think in Northern Ireland we are really heading for a very difficult situation which could, in the worst case scenario, reignite the violence."
So, it seems safe to say - at the very least - that the UK and EU are very far from a mutually satisfying agreement.