Civil servants preparing for negotiations to pull Britain out of the EU face a task of “mind-boggling” complexity, experts have said.

With the 100-day mark to be passed later this week since the UK voted to leave, there are signs of impatience among some Brexiteers at the slow pace of progress, with former Ukip leader Nigel Farage warning against “backsliding”.

But Whitehall-watchers said it was likely that Government officials have still not fully quantified the scale of the task ahead, which is likely to stretch well beyond the two-year deadline set under Article 50 of the EU treaties.

Stephen Booth, co-director of the Open Europe think-tank, said it was likely that Brexit would end up being a gradual withdrawal from different aspects of the UK’s entanglements with the EU, rather than a single “big bang” event.

The Institute for Government’s Brexit lead Hannah White said officials should be working on the assumption that finding a new trade relationship with the remaining EU will take more than two years, and push from an early stage for an interim deal to keep the wheels of trade turning in the transitional period following the end of the Article 50 talks.

Any deal reached in the talks – which will not begin before the end of this year – will have to be approved by all 27 European capitals and may be subject to legislation at Westminster, reducing the chances of a swift conclusion, she said.

“Every time we look at the different aspects of it, we see a whole new degree of complexity and new things that need to be taken into account,” Ms White said.

“First there's the process of getting to the negotiating position, which involves a lot of consultation with different levels of government and economic sectors and working out what trade-offs and compromises you can accept. Then there’s the process of negotiating the divorce agreement, then working out the new trading and immigration arrangements we want with the EU.

“Before getting a trade agreement with anyone else, we need to sort out our baseline position with the World Trade Organisation, which involves negotiations affecting all sorts of sectors and could take years. Other countries need to know what our basic offer is within the WTO before they strike a free trade deal with us. For the US it's a legal requirement that a country’s WTO schedules are agreed before they can enter trade talks with them.

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“I think it’s highly unlikely we will have a trade deal sorted out with the EU by the end of the two-year Article 50 process. We will need some sort of interim agreement, and there have been suggestions we should sort that out before triggering Article 50, though the EU may prefer to keep pressure on the negotiation process by not agreeing an interim deal in advance.

“We can spend as long as we like coming up with a deal centrally, but when it has to be approved by all 27 EU states all sorts of national and sub-national interests and lobbying will come into play. The sequencing of it all is really mind-boggling.”

Meanwhile, upcoming events in the European calendar will create extra time pressures, such as the European Parliament elections and the appointment of a new EU Commission in 2019 and the need for a new seven-year EU budget in 2020.

Although the UK may not formally have left the EU by this time – especially if Ms May chooses to delay invoking Article 50 until after German elections in the autumn of 2017 – there is unlikely to be any appetite for Britain to elect new MEPs or appoint a commissioner. The remaining EU states can be expected to draw up their new multi-annual financial framework to reflect the UK’s likely absence, even though some legacy commitments will see Britain making payments into the budget beyond 2020.

Mr Booth said that the size of the UK’s economy and its position as a key member of both the UN Security Council and Nato should enable Ms May to achieve her goal of an “ambitious” bespoke deal for Britain, rather than the off-the-shelf models in place with Norway or Switzerland. This may mean Britain continuing to co-ordinate closely with the EU after Brexit on security issues, such as sanctions on Russia, he suggested.

“There are lots of process issues at the EU level where it would make sense for the UK to be actively extracting itself at a particular time,” said Mr Booth. “But these issues aren’t necessarily the same as sorting out the key questions of whether we stay in the customs union and what will be the exact trading relationship between the UK and EU, which may be a longer process.

“I think the UK will have to see it as a process rather than an event. One of the things the Government should be looking at is whether there can be an early agreement about a less time-pressured negotiation.”

While Ms May was right to “bide her time” over Article 50, she will face growing political pressure to take concrete steps towards the exit, he predicted.

Ms White said that calls for a “hard Brexit” which would see the UK pull out of the EU without negotiating new trade deals was “simplistic”, potentially exposing agriculture to cheap imports and imposing “punitive” obstacles to market access for some exporters.

Leaving the customs union would create a sudden demand for hundreds of customs officers as well as the logistical problem of finding space in ports like Dover for huge numbers of containers which would need to be checked.

The UK would also be exposed if it leaves the EU before finalising a new trade relationship and relies on an interim arrangement to tide it over. Food-exporting countries like Russia or Argentina would be likely to object to the WTO over such a deal granting protections against cheap imports to a non-EU member.