Hammond revealed the UK would look for a "quick and simple" and "ambitious agenda for a comprehensive free-trade agreement" in the House of Commons, while May's landmark address at Lancaster House said the UK "cannot" remain a member.
Hammond said: “We will go forward understanding we cannot be members of the Single Market because of the political lines around the four key freedoms that the other leaders have set.”
Read more: LIVE: Theresa May outlines her Brexit plan
He added that the UK would be "banging our heads against a brick wall" if it tried to overcome this resistance.
Hammond said the banking sector will have an "enhanced equivalence regime" rather than an extention of the current passporting regime.
Speaking separately, May concurred that remaining a Single Market member would mean complying with the rules around the market, without being able to contribute, and keeping the UK within the jurisdiction of the European Court of Justice.
"It would to all intents and purposes mean not leaving the EU at all," she said.
"And that is why both sides in the referendum campaign made it clear that a vote to leave the EU would be a vote to leave the Single Market."
May also set out promises to allow MPs and peers a vote on the final terms of a Brexit deal, and to offer businesses a "phased" move to Brexit.