There's still 3 basic options: Hard (full) Brexit, Soft (partial) Brexit, and No Brexit.
The current government (Conservative/DUP) favour Hard Brexit - the main opposition (Labour and some Conservatives) favour Soft Brexit, while others still (e.g. SNP) favour No Brexit.
However, no-one has the guts to fully support No Brexit because there are simply too many people who want it (i.e. 52% of the UK population), so it is politically suicidal to favour No Brexit, hence why the main opposition favour 'Soft Brexit' (which involves coming out of the EU, but remaining in the Customs Union and European Single Market). The big problem with that option, however, is that not only do a lot of British people not want it, but the EU is also pretty solidly against it - they call it the 'Cake' approach (as in "you can't have your cake and eat it"), arguing that continued Single Market access (for which the current Customs Union is required) is a privilege of EU membership.
The Conservatives are also in a bind because their leader, Theresa May, wanted to Remain in the EU, and like some other Tories, she also seems to be in favour of what looks very like Soft Brexit i.e. leaving the EU but striking a favourable deal with the EU that will essentially mean retaining Single Market access but without sticking to the current Customs Union (favouring instead the creation/negotiation of a new customs union), which, ironically, is precisely what the Labour party are asking for now as well. But, those who favour Soft Brexit are likely going to be disappointed because the EU itself will make it nigh on impossible for such an outcome to occur, because (unsurprisingly) they want to show that a member state that leaves the EU will lose all the benefits that come with full membership, which includes tariff-free Single Market access.
But Labour could force the issue by basically beating the government on the main decisions that will have to be passed by parliament, and perhaps even forcing a new election that could see Labour take power. The Tories have to balance the fact that their core support wants nothing less that Hard Brexit, but that their core support is not strong enough to deliver a clear majority in Parliament, and that if Labour can convince enough people that Soft Brexit is the way forward (in spite of the fact that it is practically impossible to achieve), then the Tories could be kicked out before they can deliver Hard Brexit. But, the trouble is that no matter what the British people want (which increasingly looks like Soft Brexit/a cherry-picked sweet deal/the 'cake and eat it' idea) will be met with derision and anger from the EU - in other words, no matter which way you slice it, Soft Brexit will not happen. I also don't think that No Brexit will happen - not least because there are too many people in the UK who want out, but that basically leaves us with a situation where we face Hard Brexit but possibly without a government capable of delivering it.