Normally, Parliament sits for one year, but officials said more time will be needed.
Here are the key questions surrounding the Brexit negotiations.
Both sides are keen to ensure that people and goods keep moving smoothly across the border and that nothing undermines the peace agreement that ended decades of bloody conflict in Northern Ireland.
The negotiations have been billed as the most complex in Britain's history as it unravels 44 years of membership and its threat to walk out with no deal in place has anxious European capitals. May has clung on to power but has so far failed to conclude an agreement with Northern Ireland's ultra-conservative Democratic Unionist Party that would bolster her ability to govern.
The BBC has been told by European Union sources that the talks will follow the EU's preferred pattern of exit negotiations first, with the future relations between the two sides - including the free trade deal the United Kingdom is seeking - at a later date.
The divorce bill will involve its commitments to the EU's 2014-2020 budget, as well as ending its membership of European Union institutions, banks and funds like the Turkey refugee facility.
Mr Hammond told the BBC's Andrew Marr Show that having no deal would be "a very, very bad outcome for Britain" but added that one that aimed to "suck the lifeblood out of our economy over a period of time" would be even worse.
Other issues to be discussed include future arrangements on security co-operation and intelligence sharing once Britain is outside the structures of the EU.
Formal negotiations on the terms of Brexit finally begin on Monday, some 361 days after the European Union referendum of June 23 2016.
Still trying to shore up her authority after last week's election calamity injected new uncertainty into Britain's path to leaving the European Union, May is sending her Brexit Secretary David Davis to Brussels on Monday to launch the process with EU negotiator Michel Barnier.
HSBC, which has 43,000 employees in Britain, said in January that it was planning to move "activities covered specifically by European financial regulation" to the EU, which would shift about 1,000 jobs out of the UK.
Many in Britain have seen the election result as repudiating May's threats to walk away without a deal. A second phase of talks on future trade relations will follow only after they are satisfied that sufficient progress has been made on these issues.
For another, the combination of finally launching talks on Monday and May being at the summit on Thursday and Friday made the coming week a key opportunity to "rebuild trust" after tempers had boiled over on both sides in recent months.
He added that he was approaching the negotiations in a "constructive way", given the fact that they will be "difficult at points".
Winter/spring 2018/19 - The European Court of Justice could be asked to rule on whether the deal requires approval by each EU state. If so, it could have to be ratified by up to 38 national and regional parliaments, with any of them effectively holding a veto.
The Westminster vote will take place before the European Parliament debates and votes on the deal, effectively giving MEPs the final say on whether it will go ahead.
Almost a year to the day since Britons shocked themselves and their neighbours by voting on June 23 to cut loose from their main trading partner, and nearly three months since Prime Minister Theresa May locked them into a two-year countdown to Brexit in March 2019, almost nothing about the future is clear.
This date can be extended by agreement between all member states.