London - Boris Johnson and Jeremy Hunt, the two candidates to be Britain's new prime minister, have both promised to deliver Brexit where Theresa May failed.

Yet they face the same political constraints, both at home and with the EU officials in Brussels.

- Ticking clock -

Britain is due to exit the European Union on October 31, leaving only a few months for the new premier to grapple with the issue.

Boris Johnson says Britain must leave by this date, after May twice delayed Brexit in a failed attempt to get the Withdrawal Agreement she agreed with Brussels through parliament.

Jeremy Hunt has also promised to deliver Brexit as quickly as possible, but has left open the option of a short delay if a deal with the EU is within reach.

Both have refused to rule out leaving with no agreement on the divorce terms -- a potentially damaging "no deal" Brexit -- if necessary.

How does Britain leave the European Union?

- Parliament deadlocked -

MPs in parliament's lower House of Commons rejected May's Brexit deal three times, but also voted against leaving with no agreement.

The new premier must find some consensus, starting by uniting his divided Conservative party.

He will also need to win back the support of the Democratic Unionist Party (DUP), Northern Ireland's biggest party.

Since losing their Commons majority in the 2017 general election, the Conservatives have relied on DUP support to govern.

But the DUP rejected May's divorce deal over its arrangements for Northern Ireland.

How did Britain vote in the Brexit referendum?

- Brussels firm -

Both candidates have said they will seek to amend the Northern Ireland "backstop", which is also a major concern for many Conservative MPs.

It would keep Britain in the EU's customs union and create a special regulatory status for Northern Ireland in order to keep open the border with the Republic of Ireland.

Brussels has repeatedly said it will not reopen the divorce text.

However, it is willing to change an accompanying Political Declaration outlining the potential UK-EU future trade and security relationship.

EU's Tusk warns next British PM

- No deal risks -

May abandoned her threat of a "no deal" Brexit after accepting that parliament would seek at every turn to block such a scenario.

Many MPs and business leaders fear an abrupt break with Britain's largest trading partner would lead to significant economic disruption.

But it remains the legal default position and the new premier could still do this on October 31 by declining to seek a new delay.

It might also happen if EU leaders refuse to agree unanimously on another Brexit extension, something some of them have warned might happen without some political breakthrough in London.

MPs determined to prevent no-deal would be forced to call a confidence vote to bring down the government to stop him, which would likely trigger an immediate general election.

Many Conservatives fear such a poll, after winning just nine percent of the vote in elections for the European Parliament in May.

Brexit explained in 8 graphics (slideshow)