While Brexit minister David Davis on Monday stressed that Britain would have to quit the EU's common market and customs union, Hammond agreed with Carney on the need for a transitional deal "to avoid unnecessary disruption and risky cliff edges".
The bloc would first seek to reach an agreement on European Union citizens rights, the UK's departure bill, and the future border between the Republic of Ireland, an European Union member, and Northern Ireland, a British region.
Anxious by immigration and loss of sovereignty, Britons voted past year to end their country's four-decade membership in the 28-country bloc - the first nation ever to do so.
The UK Government said in a press release that Davis is "confident that he can get a positive outcome and secure a new deep and special partnership with the European Union".
The UK chancellor said he would not agree to a deal that would "destroy" Britain just hours before the official Brexit negotiations begin. But it must be done in a way that works for Britain ...
He spoke about the need for a new system to allow British and European Union banks to do business with each other after Brexit, to avoid splitting markets.
Instead of having a slim majority in Parliament, May's Conservative Party lost 13 seats, and with it their majority power.
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There will be bogeys out there, but this week is going to come down to someone shooting one or two low rounds on the weekend. It's a 6,841-yard, par 70 that allows players to shoot for the pins, with the victor usually in the high teens under par .
"In the first step, the negotiation rounds will be broken down into three groups - citizen rights, the single financial settlement, and other separation issues".
Speaking to the BBC's "Andrew Marr show", Mr Hammond said: "No deal would be a very, very bad outcome for Britain, but there is a possible worse outcome and that is a deal that is deliberately structured to suck the lifeblood out of our economy over a period of time". They are due to give a joint news conference after talks among their teams lasting seven hours.
European Union officials had earlier warned May not to make that offer so early in the talks.
Meanwhile, German Chancellor Angela Merkel yesterday urged the EU's remaining 27 members to stick together during the Brexit talks.
Mr Hammond said: "We recognise that this is a negotiation, and our negotiating counterparts, while broadly sharing our desire for a close ongoing relationship, will have their own priorities".
"I would like us to get a good agreement that is in both sides' interests".
The two men will meet for a week every month to negotiate, and use the time in between to "work on proposals".
However, Britain rejected the two-stage negotiating arrangement, insisting that the talks on trade relations should take place "in parallel".
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