The 6 possible models for Theresa May's Brexit Britain

Prime Minister Theresa May has insisted that she won't give a "running commentary" on Brexit negotiations, and that means few people know what kind of deal she favours when the country does leave the European Union.

She has indicated that it is like to be a "hard Brexit," due to her prioritising immigration curbs over keeping Britain within the Single Market - a free trade agreement between EU countries and several others - but has so far not said what might replace it.

A new report by Brexit research group "The UK in a Changing Europe" has outlined six deals that the UK could pursue after it formally leaves the EU - which May has set a March 2019 deadline for.

Here is what it looks like:

Problems with a 'soft' Brexit

The report says that the "least economically risky" model would be to have a status "similar to Norway, participating in much of the Single Market, perhaps with some new curbs on free movement of labour."

There are several problems with a "pure Norway" model, however. Firstly, as the report says, "another prominent claim in the referendum campaign was that the UK would gain from no longer having to contribute to the EU budget, yet Norway continues to pay a membership fee."

Secondly, EU officials have already made it very clear that the UK will have to accept free movement of labour if it wants access to the Single Market.

That is possibly why May has already explicitly ruled out a "Norway model" for the UK.

Problems with a "hard Brexit"

At the other end of the spectrum, May faces a different set of problems. If the UK falls back on standard World Trade Organisation (WTO) rules, it would have the same access to the EU market as China, which means very high tariffs. The report warns that even standard WTO membership isn't a guarantee, however, and suggests that the UK may need to reapply to join the WTO once it has left the EU.

That is unlikely, however. WTO chief Roberto Azevedo said last week that "the UK is a member of the WTO today, it will continue to be a member tomorrow. There will be no discontinuity in membership."

The reality is that Theresa May will have to try and find a compromise which allows some access to the single market and curbs on immigration, but that will be difficult given the demands placed on her by a group of European officials and leaders who believe the UK must "pay the price" for Brexit.

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