Both sides admit there are significant differences to be overcome and are locked in a standoff
over the structure of the talks.
Neither the UK nor the EU wants to talk about what will happen if there is no deal, but some British Members of Parliament believe it is time for the government to start talking seriously about what would happen in this scenario.
The UK's chief Brexit negotiator, David Davis, insists
that "concrete progress" has been made. He has received assurances on healthcare rights for British citizens living in the EU and on arrangements for sharing data. But he has admitted the talks are "tough and at times confrontational."
His EU counterpart, Michel Barnier, has said there has been "no decisive progress on any of the principle subjects" and he is "disappointed" at the British approach. He is insisting that there must be sufficient progress on the the issue of whether or not there will be a hard border between Ireland and Northern Ireland
, the rights of EU citizens in the UK and the Brexit bill before any discussion of a future trade deal.
Davis says such matters can only be decided as part of the discussions on the post-Brexit relationship. He points out it is impossible to resolve questions such as the Irish border
without considering future customs arrangements.
At next month's summit in Brussels, the EU is due to declare whether there is sufficient progress on what it calls "separation issues" to begin talking about post-Brexit trade.
But senior figures in the European Parliament are already suggesting the assessment should be delayed until December.
Sources close to the talks have suggested Prime Minister Theresa May could use the occasion to appeal directly to EU leaders to try to break the stalemate. But the remaining 27 EU states are clearly reluctant to unpick their carefully negotiated joint approach to the talks.
The EU does have a tradition of somehow finding a compromise at the eleventh -- or even the thirteenth -- hour, and it is in the interests of both sides to reach a deal. But we are constantly reminded that the clock is ticking and the gulf between the two sides on so many critical issues remains as deep as ever.
Both sides want a transition period so there is no "cliff-edge" for businesses and citizens. But that will only happen if there is at least an outline agreement on where that transition will lead.
Without a deal, the UK would suddenly find itself in the same position as any other non-EU country which does not have special arrangements in place with the EU. It would suddenly operate under World Trade Organization rules, which would mean tariffs and restrictions on trade with its biggest economic partner. And there would almost certainly be big problems at the borders.
There are real risks for the British government in talking up the prospect of leaving without a deal. It would face accusations of a disastrous failure. Businesses would warn of serious consequences and the pound would probably dive still further. Theresa May could struggle to retain her already precarious hold on power.
But if the negotiations continue at the snail's pace which we have seen over the past five months, we will reach a point when it becomes clear that an agreement is unlikely to be reached in time to achieve the smooth transition which the UK government is seeking.
If it has laid the ground for such a scenario, it is just possible that it may be able to contain the fallout. It could set out contingency plans, talk up the prospects of global free trade deals and lay the blame firmly at the door of an intransigent EU.
British ministers may need to demonstrate that they are seriously prepared to walk away without agreement if they are to win any real concessions from the EU.
The UK government has always said "no deal is better than a bad deal." It may need to make it clear this is not just a hollow threat if there is to be a breakthrough in the complex and tortuous Brexit negotiations.