Two polls published during the course of the last few days have approached the question of what kind of Brexit voters would like very differently. At first glance, they also appear to have produced two very different sets of results. But on closer inspection they may be thought to point in much the same direction.

The first exercise comprises a large online poll conducted by Lord Ashcroft. Inter alia, this poll asked its respondents how important they thought it was that each of four possibilities should form part of the terms of the UK’s withdrawal from the EU. The four possibilities were tariff-free trade, the UK no longer paying into the EU budget, the UK no longer being under the jurisdiction of the European Court of Justice (ECJ), and the UK having some control over migration from the EU.

The second poll is a smaller, but still interesting exercise conducted for the Polling Matters podcast by Opinium. Instead of asking people what they wanted to see included in any Brexit deal, it invited them to consider how they would feel if various outcomes were not delivered by Brexit. Amongst the outcomes addressed by the poll were the same four subjects covered by Lord Ashcroft: no longer having unrestricted access to the single market, the UK still making a financial contribution to the EU budget, the ECJ still having some jurisdiction in the UK, and no significant reduction in the level of immigration.

The results of Lord Ashcroft’s poll echo our own survey work in that they suggest there is substantial support for free trade but at the same time majority support for curbing immigration. On a scale from 0 to 100, where 0 denotes that it is ‘not important at all’ for that item to form part of the terms on which Britain leaves the EU and 100 indicates it is ‘extremely important’ that it should, avoiding tariffs secured an average score of 73 and being able to control EU immigration 60. At the same time the poll also confirms there is little enthusiasm for continuing to pay contributions into the EU budget. That received an average score of 71, while not being subject to the jurisdiction of the ECJ, 64.

However, as we might also anticipate from our own previous research, these items varied in the extent to which Remain and Leave voters espoused different views about their importance. In the case of immigration, the EU budget and ECJ jurisdiction, the average score given by Remain voters was around 30 points lower than that given by Leave voters. They are clearly all issues that exercise Leave voters to a greater extent than they do Remain supporters.

At the same time, however, even Remain voters gave immigration control a score of 46, suggesting that many of them would also like to see an end to freedom of movement. Equally, they also gave ending the jurisdiction of the ECJ an average score of 50, suggesting that sovereignty is an issue for many of them too. Here, then, in this poll is yet further evidence that some Remain voters share some of the concerns about immigration (and sovereignty) that are widespread amongst Leave voters.

However, when it comes to tariff-free trade there is no disagreement between Remain and Leave voters. Both groups give the issue a score of 74. As we have argued elsewhere, achieving that goal is evidently regarded as desirable across the referendum divide.

But at the same time, of course, between them these results also imply that for many Leave voters free trade is relatively less important than other objectives. Thus in Lord Ashcroft’s latest poll as many as 66% of Leave voters think that immigration control is more important than access to the single market, while only 19% take the opposite view. In contrast, the equivalent figures amongst Remain voters are 19% and 57% respectively. These findings are in line with those in many a previous poll on the supposed trade-off that will face the UK in the negotiations – but it should be remembered that what they show is not that Remain voters are necessarily opposed to immigration control, but rather that they just consider it to be less important than free trade.

(Intriguingly, however, the overall proportion prioritising immigration has fallen since Ashcroft previously asked the same question last August. Then 52% prioritised immigration control and only 28% single market access, in what was admittedly an unusually high imbalance in favour of immigration control as compared with other polls. This time the numbers are 42% and 24% respectively. The shift appears to have been on a similar scale amongst Remain and Leave voters.)

But what of Opinium’s poll for Polling Matters? That poll finds that voters are seemingly evenly divided about free trade. As many as 40% reckon Brexit would still have been worth it if free trade is not secured, while 42% say Brexit would not have been worth it. In contrast, as many as 62% say that Brexit would not have been worth it if Britain were still paying into the EU budget, while 58% said the same of the ECJ, and 56% immigration control. In short, whereas free trade emerges as the most popular of the four objectives in Ashcoft’s poll, here it emerges as seemingly the least important.

There is also another important difference between the Polling Matters and the Ashcroft poll – they paint a completely different picture of what divides Remain and Leave supporters. Whereas Ashcroft finds that Remain and Leave voters had similar views about free trade and different views about the EU budget, the ECJ and immigration, the Polling Matters poll reports entirely the opposite pattern. In the latter poll, Remain voters were almost as likely as Leave voters to say that Brexit would not have been worth it if Britain were still paying into the EU budget, were still subject to the ECJ, and had not experienced a significant reduction in immigration. In contrast Remain voters (66%) were much more likely than Leave voters (20%) to say that Brexit would not have been worth it if Britain no longer had unrestricted access to the single market. A similar gap between the two sets of voters is also evident in response to a further item in the poll on whether Brexit would have been worth it if there were a recession and significant job losses

To make sense of why the Polling Matters poll reports such a different pattern, we need to remember that the disagreement between Remain and Leave supporters is about relative rather than absolute priorities. What the poll reveals is that, given that the UK is to leave the EU, even many a Remain voter hopes that leaving will at least deliver what its advocates claim it will deliver. Immigration control and sovereignty are not necessarily regarded as such an anathema by Remain voters that they recoil from them with horror. They just hope they can be achieved without damaging the UK’s economic position. Leave voters share the same hope that all four key objectives can be achieved – it is just that they are more likely to be willing to take an economic hit if that is indeed what Brexit brings.