Lawson said that people voted in large part for Brexit due to immigration, and as such the UK must move away from the doctrine of free movement, as the democratic will of the people should be respected.
"I respect the democratic view of the British people, which was very clear in the referendum," Lawson told BBC Radio 4's Today programme.
"The British people voted very clearly to leave the EU and they voted in part to get away from the doctrine of the free movement of people.
"It is the responsibility of the government, which I'm sure Theresa May fully accepts, to decide how best to implement the democratic view of the British people.
"That means in practice that we accept [Europe's] view that you can't be inside the Single Market unless you accept freedom of movement and since that is not on we shall be outside of the Single Market. It is as simple as that."
The comments from Lawson come as May chairs a cabinet Brexit meeting at Chequers, the Prime Minister's country house north of London.
May said before the meeting: "We must continue to be very clear that “Brexit means Brexit”, that we’re going to make a success of it. That means there’s no second referendum; no attempts to sort of stay in the EU by the back door; that we’re actually going to deliver on this."
May has said that Article 50 won't be triggered this year, meaning formal negotiations with fellow EU member states will not begin until 2017.
Lawson added that the UK will not need to "waste time trying to negotiate elaborately a special trade deal with the EU" as it too is not on and not necessary, given that large amounts of trade takes place with the rest of the world.