David Davis, the UK cabinet minister who leads the Brexit negotiations, arrived in Brussels on Monday afternoon for the third round of negotiations on the UK’s exit from the EU. Both he and Michel Barnier, the EU lead negotiator, made a media appearance ahead of talks commencing and it was clear that the focus of each side remains very different. For the UK it is about the future trade arrangement, for the EU it is about agreeing the terms of leaving first. With the heads of state due to meet in October to assess progress on this before moving onto the next stage, time is running out.

Assuming that the negotiators can get over this first hurdle, and that could well take more than this week’s talks, the fault lines between the EU and UK are becoming clearer, but the route to reconciling them remains unclear.

The Labour Party provided a twist to the Brexit debate in the UK at the weekend, with the announcement of a new policy that would see the UK remain part of the customs union and single market for a transition period, and accepting the current rules for membership. It also held out the possibility of long-term participation, if it could reach a satisfactory arrangement with the EU on migration. This will make the passage of the repeal bill in the UK Parliament his autumn, where the Government has a wafer-thin majority, very interesting indeed.

The success of the Scottish Conservatives in the last general election means that it will have a strong voice in the passage of this legislation. Instinctively it is pro-EU, but overall the Conservative party in Westminster are committed to what is described as a hard Brexit.

All of the position papers published so far indicate that the UK wants to retain all of the present trading arrangements, while at the same time following the three big ideas of the Brexit ideology. These are taking back control of the borders, meaning an end to the freedom of movement of people with the EU, making its own trade deals outside the EU framework and withdrawal of jurisdiction of the European Court of Justice, the ECJ.

On the ECJ, the UK position paper did demonstrate some flexibility in thinking, by tabling the ‘Mantua option’ – which is arbitration followed by referral to the ECJ for final ruling.

Even on the thorny issue of the “Brexit bill” the UK Foreign Secretary, Boris Jonson, has moved from his earlier position of suggesting that the EU “go and whistle” to a recognition that there would be a cost that had to be met. The Brexit bill is one of the EU red line issues, so it is possible to visualise some movement on it and the ECJ issue, despite murmurings of a reluctance by the UK to provide its methodology for calculating.

It is impossible to reconcile the present UK and EU negotiating positions on trade and people movement without a hard border on the island of Ireland. The UK position paper was idealistic in stating that it would not be responsible for imposing a border of any sort, never mind a hard border. Just how an open Irish border with an equally open Ireland to citizens of the other 26 members of the EU fits, is impossible to explain. It could be claimed that employment records and registration for social services would act as a control.

While that may be, in turn that would created a huge undocumented economy, similar to what has existed in the US for several decades. Low-paid jobs would attract workers who would operate outside the system without the protection of employment law and, more importantly from a UK perspective, be completely unknown to the authorities. At least the present official entry system provides a measure of control, with its checking of passports at the point of entry. Therefore, the UK position paper on the Irish border arguably puts it in a position with even less control on the movement of people into the UK.

On the movement of goods, it is the EU that will be imposing checks, as the Irish border will be only a land frontier between the UK and EU. If the UK is trading with other third countries, then it is impossible to visualise the EU allowing the Republic of Ireland to be a back door into the other 26 members for products.

It is also difficult to visualise how a “fudge” can be found that satisfies both parties on something as definitive as being part of the customs union. Even in what the UK considers an ideal arrangement – a comprehensive free trade agreement (FTA) – there remains the issue of border controls.

The Canadian-EU agreement, often presented as the ideal FTA, still has border controls and strict quota allocation for sensitive agricultural products, such as beef and dairy. Adherence to agreed standards has to be demonstrated and quotas complied with. Also in this “ideal” outcome, the cost of doing business was estimated to increase by 5% in work carried out on behalf of the UK regional agriculture departments.

Many positions have been stated on the EU and UK sides, but negotiations are only just beginning. The publication of the UK Labour Party’s alternative position also means that there is a way to go within the UK before a final position on what it will settle for is fully decided.