A large majority of the British public want the UK to retain at least “full access” to the EU’s single market after Brexit, a new poll has revealed.

The exclusive survey for The Independent showed backing for full access as the lowest level of integration has increased steadily this year and has now surpassed 60 per cent.

The public’s clear and growing desire to retain such a high level of access to the market heaps pressure on Theresa May as she prepares for a critical EU summit at which an outline Brexit deal may be agreed.

The Independent understands the EU is preparing to offer the UK a Canada-style free trade agreement that would not deliver the “frictionless” trade Ms May is seeking, and is something that just a quarter of people said they wanted in BMG Research’s poll.

The prime minister is also to meet with her cabinet ministers next week when it is likely she will discuss tweaks to her Chequers proposals to make them more amenable to the EU’s negotiators, including the possibility of a much closer customs union.

Pollsters asked a weighted sample of more than 1,500 people what their preferred option would be, including…

Full EU membership with no limits on immigration

Full single market membership, similar to remaining in the EEA, with moderate immigration limits

Retaining “full access” to the single market with completely new immigration rules

Seeking a free trade deal with a degree of access to the single market and stricter immigration controls

No free trade deal with strict immigration rules, effectively the WTO option

More than 61 per cent of people opted for one of the first three options, all of which deliver full access to the single market, with 22 per cent of the total within that proportion wanting to just stay in the EU.

Question from October’s BMG Research poll for The Independent

Just 25 per cent said they backed the kind of free trade deal advocated by Brexiteers and several members of the cabinet, while only 14 per cent advocated a no-deal withdrawal.

Support for full access to the single market has been the majority position for months, something which has no doubt informed Ms May as she negotiated, whilst also attempting to deliver on concerns about immigration.

But BMG surveys carried out for The Independent in recent months have clearly shown support for remaining closely tied to the single market increasing, during a period in which businesses have more consistently raised the alarm about the potentially devastating consequences of rowing back from it.

Since July, backing for at least full access to the single market has risen five points, from 56 per cent.

At that time support for a free trade deal approach was at 28 per cent, while a no-deal approach had the support of 16 per cent – meaning voters have become progressively wary of both options that deliver looser ties with the UK’s biggest trading partner.

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It could make life difficult in Brussels on 17 and 18 October, when EU leaders are said to be preparing to offer the UK something closer to a Canada-style trade deal, which would not deliver frictionless trade.

Instead it would seek to reduce barriers as far as possible for a nation outside the single market, and would include clauses that leave open the possibility of further change after Brexit day, meaning a future Tory or Labour leader could tighten the relationship.

However, since the beginning of negotiations the EU’s conception of a free trade arrangement has been contingent on Ms May accepting different customs arrangements in Northern Ireland and mainland Britain, something she has already ruled out.

The Independent reported last week that the prime minister was instead considering a tighter customs arrangement than previously countenanced, along with new concessions in relation to future European regulation, which are likely to be discussed by ministers in the coming week.

Today’s new poll also saw respondents asked if tighter customs arrangements than those originally envisioned by Ms May was a concession worth making to secure a deal.

Most people – 38 per cent – said it was, with 27 per cent saying it was not and 34 per cent saying they did not know.

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Asked the same question about whether people would support accepting more EU regulation in the future, the numbers were tighter – 34 per cent backed it as a way of securing a deal, 32 per cent rejected the idea and 34 per cent said they did not know.

But the poll did suggest the prime minister has the moral support of the country going into the new summit, with a majority of 53 per cent saying that up to now EU leaders had failed to treat the UK government with respect, while a majority of 51 per cent said Britain had shown respect to EU leaders.