LONDON (REUTERS) - British Prime Minister Theresa May reappointed most of her ministers on Sunday (June 11) but brought a Brexit campaigner and party rival into government to try to unite her Conservatives after a disastrous election sapped her authority days before Brexit talks begin.

She is seeking a deal with a small Northern Irish party so that she can stay in power.

Below are a list of key dates faced by May in the coming week.

MONDAY, JUNE 12

- Northern Ireland talks

The DUP and Irish nationalists Sinn Fein are due to restart talks to form a new power-sharing government in Northern Ireland and avoid devolved power reverting to the British parliament in London for the first time in a decade.

The sides have until June 29 to secure a deal, but observers fear any concessions to the DUP by May's Conservatives could complicate the talks, deepening the region's political crisis.

- May's top team of ministers to meet

May has confirmed five of her most senior ministers will remain in their pre-election roles. She has kept in place her broader team of ministers too, with only a few changes.

Defence Minister Michael Fallon said on Sunday the Cabinet would meet "early next week". Cabinet meetings usually take place on a Tuesday but British media have reported it could meet on Monday.

- May meeting with Conservative lawmakers

May is due to meet with Conservative lawmakers in parliament. The chairman of the influential 1922 Committee of Conservative lawmakers Graham Brady has told BBC radio's Westminster Hour programme that the meeting has been brought forward to Monday.

British media have reported that moves were afoot within May's party to dislodge her after her election gamble - aimed at increasing her party's majority in parliament ahead of Brexit talks - backfired.

A leadership contest can be triggered if 15 per cent of the Conservative's 318 lawmakers write to Brady saying they no longer have confidence in May.

TUESDAY, JUNE 13

- May to meet with DUP leader Arlene Foster

Discussions were held between May's Conservatives and the DUP over the weekend with a view to the Northern Irish party supporting May's minority government on key votes in parliament.

Foster is due to travel to London on Tuesday to meet May to discuss the details of a possible arrangement.

- May to travel to France to meet President Emmanuel Macron

Brexit will likely be on the agenda at the Paris meeting, after May confirmed she will stick to the timetable of negotiations over Britain's departure from the European Union due to start on June 19.

- Parliament returns to elect Speaker

Parliament reconvenes following the national election to elect a Speaker for the lower house, the House of Commons. Swearing in of lawmakers will then begin, and continue for the rest of the week.

THURSDAY, JUNE 15

- Bank of England's Mark Carney and Finance Minister Philip Hammond speak

The two men in charge of Britain's economy deliver their annual Mansion House speech on Thursday when they are likely to try to calm businesses and investors worried by May's precarious grip on power and the uncertain outlook for the UK economy which has lost a lot of its momentum of 2016.

MONDAY, JUNE 19

- Brexit talks begin

Talks on Britain's exit from the European Union are due to begin. May has said her government will go ahead with these discussions as planned.

- State opening of parliament and Queen's Speech

Parliament is due to be formally reopened. Queen Elizabeth will deliver the "Queen's Speech", setting out the government's plans for the new parliamentary session.

The debate on the Queen's Speech usually lasts about five or six days. The vote at the end of this debate is considered an important symbolic test of the ability of a government to command the confidence of the House of Commons.

If May can get through this vote with the help of the DUP she can continue in government. If not, the opposition Labour Party would expect to have an opportunity to put forward an alternative Queen's Speech and see if it could win the support of a majority in parliament.

If neither party can command a majority in parliament for their Queen's Speech, it is likely a fresh election would be called.