The Reality Check team looks at some of the claims and promises made during the campaign by Leave campaigners who now appear to have modified their positions.
The campaign claim: Immigration levels could be controlled if the UK left the EU. This would relieve pressure on public services.
The current claim: Immigration levels can't be radically reduced by leaving the EU. Fears about immigration did not influence the way people voted.
Reality Check verdict: During the campaign, some Leave campaigners sent a clear message that the referendum was about controlling immigration. Some are now being more nuanced, saying the UK's decision to leave the EU would not guarantee a significant decrease in immigration levels.
Immigration was the key issue of the EU referendum campaign, and Vote Leave's focus on it was a key part of their strategy.
One of the main claims of the campaign centred around control of immigration levels.
Responding to the latest Office for National Statistics (ONS) figures, which showed that overall net migration stands at 333,000, MEP Nigel Farage said: "Mass immigration is still hopelessly out of control and set to get worse if we remain inside the EU."
Though Mr Farage was not part of the official Vote Leave campaign but campaigned in favour of leaving the EU, similar claims were later echoed by Vote Leave campaigner Gisela Stuart.
She said voting to remain meant there would be "no control" over migration from the EU, "no matter how great the pressure on schools, hospitals and housing becomes or how much wages in our poorest communities are pushed down".
Similarly, leading pro-Leave campaigner and Tory leader front runner Boris Johnson said that the only solution to the scale of immigration which the UK was facing, was to leave the EU.
He claimed a vote to stay in the union would mean people "kissing goodbye permanently to control of immigration".
The Leave campaign also repeatedly linked EU migration with pressure on public services.
On the 20 May, Vote Leave produced a document which it claimed outlined the pressure that migration from the European Union would put on the NHS - a 28% to 57% increase in demand for accident and emergency services.
As we discovered, an increasing population would put additional demand on A&E but the extent of that increase had not been demonstrated.
But in an article published in the Daily Telegraph on Monday, Mr Johnson denied a victory for leaving the EU could be linked to immigration.
He wrote: "It is said that those who voted Leave were mainly driven by anxieties about immigration. I do not believe that is so."
And speaking to the BBC's Newsnight programme on Saturday, MEP Daniel Hannan insisted the public had not been misled over how much control the country would have over immigration post-Brexit.
In a heated exchange with Evan Davis, he said: "We never said there was going to be some radical decline ... we want a measure of control".
"Frankly, if people watching think that they have voted and there is now going to be zero immigration from the EU, they are going to be disappointed."
Contributions to the EU budget
The campaign claim: We send £350m a week to Brussels, which could be spent on the NHS instead.
The current claim: The claim was a mistake, and we will not be able to spend that much extra on the NHS.
Reality Check verdict: Some of those who campaigned for Leave are now distancing themselves from this claim. Some have gone as far as admitting that it had been a mistake.
One of the most controversial claims of the campaign was that the UK sends £350m a week (or £50m a day) to Brussels, which could be spent on the NHS instead.
Vote Leave's Gisela Stuart was among those to make the claim, saying "Every week we send £350m to Brussels. I'd rather that we control how to spend that money, and if I had that control I would spend it on the NHS."
Many bodies including the UK Statistics Authority pointed out that we do not send that much a week because the rebate is deducted before any money is spent.
Over the weekend, Nigel Farage said making the claim had been "a mistake".
On Sunday's Andrew Marr Show, Iain Duncan Smith was shown a Vote Leave poster saying: "Let's give our NHS the £350m the EU takes every week," but he denied that promise had been made and said instead that the NHS would receive "the lion's share" of money that would no longer be spent on the EU.
The actual amount sent to Brussels each week in 2014 was £276m, a little over £100m of which is spent on things in the UK such as subsidising farmers and funding research, which the Leave campaign also promised to continue funding until 2020.
The single market
The campaign claim: Some on the Leave side suggested the UK does not need preferential access to the single market.
The current claim: The UK should get preferential access to the single market but will not have to accept freedom of movement to get it.
Reality Check verdict: The position has shifted from claims the UK could trade under World Trade Organisation rules to one which suggests the UK will continue to have preferential access to the single market, but at the same time having some control over immigration levels.
During the campaign, some Leave campaigners said that the UK outside of the EU would not need preferential access to the single market and would just trade under World Trade Organization rules.
This was the basis of research by Economists for Brexit, who said the UK should unilaterally remove all tariffs on imports.
But writing in the Telegraph on Monday, Boris Johnson quoted German employers' organisation the BDI as saying there would continue to be free trade and access to the single market.
If the UK wanted to retain preferential access to the single market, many European politicians say it would have to continue to accept freedom of movement.
Boris Johnson said that British people would continue to be able to live, work and study in the EU, while at the same time the UK would be able to introduce a points-based system to control migration.
Leader of the House of Commons Chris Grayling said that we would be able to have a free trade agreement with the EU while at the same time controlling the flow of people coming into the country.
The UK can certainly aim to secure such a deal.
But no country so far has managed a deal that allows full preferential access to the single market without having to accept freedom of movement.