He recognised that the UK's decision spurred a need to change how things are handled in Brussels to preserve the Union.
The UK has always maintained that the two issues go hand in hand and should be dealt with simultaneously.
In the first step, the two sides will deal with "the most pressing issues" in order to "lift the uncertainty caused by Brexit", including "citizen rights, the single financial settlement, and other separation issues". "A fair deal is possible and far better than no deal", the French former European Union commissioner said.
Part of this will include ensuring immigration is managed but not "shut down", Mr Hammond said, as he stressed that boosting growth is the only way to end the "hard slog" of austerity.
Following the speech, ratings agency Standard and Poor said it would not wait until the conclusion of Brexit negotiations before assessing the UK's creditworthiness. Yet many in Brussels fear that London has no real strategy, with May under pressure at home, still trying to close a deal with a conservative Northern Ireland party to stay in power, and facing criticism for her handling of the aftermath of a devastating tower block fire.
"The collective sigh of relief will be audible". "The benefit to our economy would be huge".
Labour's rise is seen to be backed by voters who voted to remain in the bloc, which some feel will drive Prime Minister Theresa May to seek a softer Brexit instead of a complete withdrawal from the EU.
"To do this in the context of our wider objectives will be challenging", he said. "It will nearly certainly need an implementation period, outside the customs union itself but with current customs border arrangements remaining in place until new long-term arrangements are up and running".
The EU has made it very clear that if the United Kingdom wants to keep the benefits of being part of the Customs Union, it needs to stay within the Customs Union.
"I will not, and we, the EPP, will not accept that our currency will continue to be managed there, that they will continue to conduct business with it even though they don't comply to our banking regulations anymore in Great Britain". May was preparing to sack Mr. Hammond before the general election.
Brexit secretary David Davis agreed to drop earlier demands he made last week that trade talks should run in parallel with the divorce discussions, an issue that he had promised to turn into "the row of the summer". However, Hammond made a point of acknowledging the concerns of other European Union countries about their oversight of financial markets which are vital to their economies but will be outside the bloc.