Theresa May's hopes of keeping Britain within the EU’s single market after Brexit under the terms of her “Chequer’s agreement” were flatly rejected by European negotiators this month.

With talks still mired in stalemate, the European Commission president Jean-Claude Juncker told assembled MEPs in Strasbourg: “We respect the British decision to leave our union, even though we continue to regret it deeply.

“But we also ask the British government to understand that someone who leaves the union cannot be in the same privileged position as a member state.

“If you leave the union, you are of course no longer part of our single market, and certainly not only in the parts of it you choose.”

If Britain were to leave the single market after Brexit, what would that mean for the UK? And what are the options for the country’s relationship with Europe if it exists outside that market?

What exactly is the single market?

The European single market is the most ambitious part of the whole “European project”. It aims to break down all barriers to trading across the 500 million-person area by ensuring the “four freedoms”, sacrosanct to Brussels policymakers: free movement of goods, services, capital and – most controversially - labour.

As an EU member, the UK has signed up to each of those freedoms which, as Brussels has repeatedly made clear, are non-negotiable.

Being part of the single market gives UK businesses unfettered access to 500 million customers in all states within it and in turn allows UK consumers and companies to purchase goods and services from across the continent. It eliminates tariffs and reduces costs and administrative burdens by applying one set of rules across all member states.

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The single market is different from the customs union, which ensures all countries charge the same import duties to non-members, but says nothing about free movement of labour. The prime minister has repeatedly said the UK will not maintain full access to the customs union but has so far been unable to secure an agreement on what form the new relationship might take.

Could the UK stay in the single market without having to follow all of that troublesome ‘red tape’?

No. The single market is governed by reams of legislation that aims to harmonise rules on everything from maximum working hours to what tackling climate change. Contrary to popular myth, no EU rule has ever banned excessively curved bananas (though standards for fruit quality are laid out in Commission Regulation 2257/94).

Without following unified standards, the single market ceases to be a single market as any one country can implement their own rules.

It is possible to stay in the single market but be outside of the customs union, as the European Economic Area countries (Iceland, Norway and Lichtenstein) do. This allows them to negotiate their own trade deals and to opt out of some legislation, notably fishing quotas. However, they still have to implement all EU laws relating to the operation of the single market, including free movement of people.

How big could the impact of leaving the single market be?

A huge 44 per cent of Britain’s exports go to the EU – £220bn out of £510bn – according to the Office of National Statistics. If the UK did not negotiate a favourable trade deal with the EU, those exports would be subject to import tariffs as well as extra administrative costs.

In the period before any new deal was implemented, the UK would probably have to trade on standard tariffs under World Trade Organisation rules.

An analysis by The Independent found that the cost to Britain’s exporters – in extra tariffs alone - would be at least £4.5bn per year. This conservative estimate does not include the difficult-to-measure costs of non-tariff barriers, such as the enforcement of different market standards and regulations.

What about a free trade agreement?

It is possible for the UK to have access to the single market without being a member of it, or being part of the customs union. The UK could negotiate a deal with the EU that allows access to trade freely with the bloc. The EU has 56 free trade agreements with countries around the world, and is in the process of negotiating several more.

On the face of it, this sounds like the option most amenable to many Leave voters, but it is not the simple solution it may first appear.

First, when negotiating the terms of that deal, the power balance is tipped heavily in the favour of the EU – the biggest customs union in the world by economic output. Therefore it is likely that the UK would have to agree to adhere to most of the rules that apply as a member state if it wants to trade with it. As a non-EU member it would lose the ability to influence that legislation.

Ms May’s has previously warned that it would be a “calamitous act of self-harm” for the EU to scupper a free trade pact with the UK by pushing for punitive terms. As the smaller partner, it is likely the UK would be more damaged.

In addition, such deals can take years to negotiate as all EU member states have to agree to any deal. The recent EU-Canada trade deal took seven years to agree.

Once implemented, the UK’s imports to the single market would still have to adhere to a lot of that much-maligned and misunderstood “red tape”.

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What are the positives about leaving the single market and customs union?

The main change would be that the UK would not have to sign up to the free movement of labour. Immigration has been the most divisive Brexit issue of all and clearly a large number of people voted to leave in order to see it reduced.

Others have pointed out that large parts of the economy and the NHS are hugely reliant on inward migration.

Outside the EU, the country would have the power to limit the number of migrants entering the country. The government has given little detail as to how it would deal with immigration to ensure that businesses can still recruit people with the skills they need.

A “points-based” system has repeatedly been mooted, though there are scant examples from other countries of this working effectively in practice.