May said Britain would seek an equal partnership with the EU, but would not adopt models already used by other countries that have free trade agreements with the bloc.
EU leaders have said Britain cannot try and cherry-pick the best elements of membership.
"Our approach is not about cherry-picking, but about reaching a deal which fits the aims of both sides," Davis said.
"We understand the EU wants to preserve its four freedoms, and to chart its own course. That is not a project the UK will now be a part of, and so we will leave the single market and the institutions of the European Union."
(Reporting by Kylie MacLellan and Alistair Smout; editing by Stephen Addison)
