30 June's BBC Question Time, factchecked

On the Question Time panel last night were Conservative education minister Sam Gyimah MP, Labour's shadow foreign secretary Emily Thornberry MP, UKIP’s Douglas Carswell MP, The Times columnist Melanie Phillips and comedian Russell Kane.

We've checked the panel's claims on the EU single market, why people voted to leave, the amount of money that will go to the NHS when the UK leaves the EU, and how many young people voted in the referendum.

Single market and immigration

“I believe that it is possible to negotiate a deal with the single market, without having a loss of border control.”—Melanie Phillips

Nobody knows.

If the UK government negotiates a deal to keep the UK in the EU’s single market then we may have to accept free movement as part of this. That means we still wouldn’t be able to control the levels of EU citizens coming into the country. All the non-EU countries who are part of the single market, such as Norway and Iceland, accept free movement.

Liechtenstein, population 37,000, is an anomaly. Due to its “specific geographical situation”, as such a small country it is currently allowed to have quotas on the number of people who can live and work in the country.

This was initially a transitional arrangement but the European think tank the Centre for European Policy Studies has described it as a “quasi-permanent” agreement now.

The law which allows this to happen is Article 112 of the European Economic Area agreement. It says that if a country faces “serious economic, societal or environmental difficulties of a sectorial or regional nature” that are likely to continue then “safeguard” measures may be agreed to address those difficulties.

No country other than Liechtenstein has used this to negotiate control over free movement, so it’s not clear whether the UK would be able to. The European Union has stressed since the referendum result that “Access to the Single Market requires acceptance of all four freedoms”. Angela Merkel has also reportedly said we can’t ‘cherry pick’ our arrangement.

Switzerland recently voted to cap immigration from the EU, which has been criticised by the EU as against the rules of the treaty dealing with free movement of people. The fallout over this is ongoing.

Why people voted to leave

“I don't know how many in the audience voted Brexit, but I know that all the evidence is that a lot of those who voted Brexit, voted because of control over immigration.”—David Dimbleby

It’s fair to say control over immigration was a significant concern among voters ahead of the referendum vote. Whether it was the primary reason behind their vote is difficult to say. Not only is it difficult to get data on this that we know is perfectly representative of the public, but sometimes it’s also difficult to really pinpoint what influences our actions when we vote.

Immigration was the issue voters mentioned in Ipsos MORI’s issues poll as the most important in helping them decide how to vote in the referendum .

But research published by Lord Ashcroft on referendum day found the “the principle that decisions about the UK should be taken in the UK” was named as the most important factor for Leave voters. The desire to regain control over immigration was listed as second most important.

£350 million to the NHS?

“When can we expect to see the millions of pounds promised to the NHS? Because we need it as soon as possible.”—Audience

“We will see more money going into the NHS.”—Douglas Carswell

“£350 [million]?”—David Dimbleby

“£100 million a week. At the moment, we pay £10.6 billion net to the EU. Approximately half of that, £5.2 billion, that’s £100 million a week, will go on the NHS.”—Douglas Carswell

The £10.6 billion figure is slightly out of date and the £350 million figure used by Vote Leave during the campaign is wrong.

Before the referendum, three leading economic institutes said that “public finances, even accounting for the return of the net contribution to the EU, would be badly affected [by the UK leaving the EU] as the economy would likely be smaller.”

So there may be less money available to spend on the NHS in the coming years, even if we stop paying the membership fee, if the economy follows their forecasts.

The figure of £10.6 billion comes from the Office for National Statistics (ONS) in March 2016. That’s roughly £205 million a week.

The ONS has updated these figures as they were incomplete when published. The new data shows that, by its calculations, the UK paid £10.4 billion to the EU in 2014.

The ONS also says that “the information used to calculate this figure is approximate and does not give the same level of detail on UK transactions with the EU as Table 9.9 of ONS’s Pink Book.”

The UK Treasury has more up to date estimates than the ONS, and uses slightly different accounting methods. They show we paid in £13 billion in 2015. We then receive around £4.5 billion back in funding, mostly for farmers and poorer regions of the UK. So the UK paid £8.5 billion more to the EU than it got back.

We have already looked into the membership fee the UK pays to the EU here.

£350 million a week to the EU was a figure the Vote Leave campaign used a lot throughout the referendum, pledging to spend it on priorities like the NHS if the UK voted to leave.

The figure of £350 million a week does not take into account the rebate, or discount, which the UK receives every year. We actually paid just under £250 million a week in 2015.

The UK Statistics Authority has said £350 million a week, is "not an amount of money that the UK pays to the EU each year".

Young people

“How many young people voted in the referendum? ... somewhere around 30%.”—David Dimbleby

We just don’t know how many young people turned out to vote in the EU referendum. There are no official figures on this.

Overall 72.2% of people eligible to vote did vote.

A figure of 36% turnout among 18-24 year olds was suggested by Sky. That was its own estimate of how many voted, rather than based on calculating actual votes, and was based on how likely various age groups were to vote at the last general election.

We have no idea how accurate it is. What we can say is that research featured in the Financial Times has suggested that areas with higher proportions of young people saw fewer people turn up to vote than areas with more older people.

Update 1 July 2016: We changed ‘exception’ to ‘anomaly’ to make the paragraph about Liechtenstein clearer.