The claim: The UK leaving the European Union would mean cuts to pensions, defence and the NHS.
Reality Check verdict: What, if anything, gets cut if there is a Brexit will be a matter for the government to decide.
"If we restrict our access [to the single market] we will be less well off and that obviously affects what we can spend on our public services," he said.
In the past few days, voters have been warned that leaving the European Union would have severe effects on different areas of public spending.
We've been told both by David Cameron and Labour's Tom Watson that the triple-lock protection on state pensions would be threatened.
We've had Chancellor George Osborne warning that Brexit would lead to between £1bn and £1.5bn of cuts to defence spending.
He pointed out that even if the government stuck to Nato's target of spending 2% of national income on defence, if national income fell, then so would defence spending.
And the prime minister has also warned about spending on the NHS being threatened if the UK left the EU.
Why are they making these warnings? Because economic forecasters have said that leaving the European Union would mean the economy would grow by less than it would have done. That would mean lower tax revenues for the government, which would mean it would struggle to achieve a budget surplus as promised in 2019-20.
What the government chose to do about that would be a question of policy, as David Cameron confirmed, but that has not stopped various groups having a guess.
The Institute for Fiscal Studies predicted the government would decide to delay balancing the budget, bringing in an extra one or two years of austerity at the current rate.
Labour In for Britain said the government would attempt to balance the budget in 2019-20, meaning it would need to make savings of £28bn, which would be divided equally between tax rises, departmental spending cuts and cuts to social security spending.
The National Institute of Economic and Social Research said the government would be trying to save an extra £44bn in 2019-20.
It is also possible that the government could decide not to balance the budget and borrow more instead.
There is a pretty strong consensus that the initial economic shock from a vote to leave the EU would make it harder to achieve a balance in 2019-20, although it could be smaller than some groups have predicted.
Read more: The facts behind claims in the EU debate

Jayden Stockley, Adam Rooney and Wes Burns all scored in the last 20 minutes.
"You see the goal threats we have and we've got Miles Storey to add to that," McInnes told BBC Scotland.
"Tonight I thought we were so industrious, tenacious, and played the game how it needed to be played."
Stockley's header broke the deadlock, and was his first goal for the club since signing in the summer.
Burns had sealed a loan switch from English Championship side Bristol City hours before the game, and the Welshman scored just a minute after coming off the bench.
"It was always my intention to get another striker on next to Rooney for the second period of the game," said McInnes.
"Jayden's goal is magnificent. Rooney is typical Rooney."
McInnes also hailed his defence as they kept a clean sheet for the first time in Europe this season.
"Defensively they deserves a lot of plaudits," he said. "They've taken a kicking recently with mistakes and lack of concentration.
"It was important we didn't chase the game willy nilly. We drew 0-0 here with Groningen and Shkendija and that was enough or us.
"The goal we conceded to Fola Esch, that was the goal that nearly put us out of the tournament. Although the performance was poor over there, that was the goal that gave the opposition the hope and incentive.
"It's very important to keep clean sheets at home in Europe, and I think we're capable of scoring over there which makes it more difficult for them. They have to play with that concern while they try and chase the game."
He added: "We're confident going on the road. Last week was not like us. In Europe we've picked up some good results, we've always been quite compact and disciplined and been able to counter.
"We did nothing last week apart from give the opposition hope that they could win. But tonight there was some good performances and it was a good night's work for us."
On the Andrew Marr Show, David Cameron talked about the effects of leaving the European Union.
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Aberdeen manager Derek McInnes hailed the attacking threat of his side as they beat Ventspils 3-0 in the Europa League second qualifying round.