UK Greens MEP Molly Scott Cato told this website, "We utterly reject the divide-and-conquer tactics."
The deputy was responding to an interview with the German newspaper Welt am Sonntag, in which Hammond said, "If we have no access to the European market, if we are closed off, if Britain were to leave the EU without an agreement on market access, then we could suffer from economic damage at least in the short-term.
"In this case, we could be forced to change our economic model and we will have to change our model to regain competitiveness. And you can be sure we will do whatever we have to do."
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On Tuesday, UK Prime Minister Theresa May is expected to say that Britain must be prepared to withdraw from the EU customs union in order to strike free trade deals with other countries.
She is also expected to outline her commitments to regaining control of British borders - even if that requires withdrawing from the European single market - and ending the jurisdiction of the European Court of Justice.
In her keenly-awaited address on Brexit, she is expected to call for an end to the division between Leave and Remain supporters.
A UK government source said, "The issue of the single market and the customs union will be answered on Tuesday when the Prime Minister sets out her negotiations."
Scott Cato, who sits on the European Parliament's special tax committee, said, "Hammond's threat to undermine the European social model is exactly what we feared the referendum vote might lead to.
"We utterly reject the divide-and-conquer tactics of the Conservative party. It is clear that Hammond has no mandate to take us out of the single market, much less to provoke a damaging race to the bottom on tax policy and environmental protection.
"That may be what Conservative donors want; it is not what the majority of the British people want and is not why they voted to leave the EU."
German MEP Sven Giegold, economic and financial spokesperson of Parliament's Greens/EFA group, said, "Threats and bullying can have no place in the Brexit negotiations. The negotiations have to be conducted responsibly based on friendship and keeping the common European interest in mind.
"The UK must not become a highly significant tax haven enjoying an open capital market with the EU. As European Greens, working together in the Parliament, we have always defended the highest environmental and employment standards."
He added, "We have also worked together to fight tax dumping in the interest of powerful corporations. It is only by such collaboration that we can ensure a European economy that works for the common good."
The UK will trigger article 50 of the Lisbon treaty at the end of March, paving the way for Britain to leave the EU over a two-year period.