After a bruising, eight-week leadership battle, Liz Truss and Rishi Sunak might be hoping for a little respite. But whichever candidate becomes the UK's 56th prime minister on Tuesday – the hotly-tipped Truss, the current foreign secretary, or outsider Sunak, the former chancellor of the exchequer – is unlikely to enjoy much of a honeymoon period.

The Spotlight: Battle to be Britain's next PM

Boris Johnson's successor as Conservative Party leader will be announced on Monday at 12:15 p.m. in London, meet Queen Elizabeth II in Scotland on Tuesday afternoon and be appointed prime minister before returning to London to make a speech to the nation at 4 p.m. and put the finishing touches on a new cabinet.

Following a two-month vacuum, while the next leader was selected, a raft of festering challenges await the incoming prime minister.

1. Cost of living

Britain is in the midst of an economic crisis. Inflation is rampant, energy bills are at record levels, the pound is expected to slump further, and the central bank governor has warned of a recession ahead.

There are worries that millions of people and businesses won't be able to deal with the impact of higher costs on everyday necessities, and polls suggest millions may refuse to pay bills. Campaigners, including former Prime Minister Gordon Brown, have warned that unless the new leader takes action, millions of households will be forced into fuel poverty, with annual energy bills of 3,500 pounds ($4,000) expected for the average family.

How the incoming prime minister approaches the crisis could define their premiership, and whoever wins will need to act fast. 

Truss has remained tight-lipped about her plans but promised she would not implement tax rises or energy rationing. She is expected to put forward a mix of tax cuts and support based on long-term borrowing in a package worth up to 100 billion pounds, according to reports on Sunday. Sunak has set out some plans for relief on energy bills via tax rebates and grants.

On their wider plans for the public finances, Truss and Sunak have sharply different visions, which have led to sharp exchanges. 

Truss wants to cut a series of taxes, make the government smaller, pull back on green commitments and raise spending on defense. Sunak argued throughout the campaign that her plans are reckless.

2. Public services

With inflation soaring to above 10 percent, many workers in the UK are experiencing real-terms pay cuts. Partially in an attempt not to fuel further inflation, the government is encouraging only moderate pay rises in the public sector. 

A series of strikes are expected over the coming months. Both Truss and Sunak told Conservative members they would take on trade unions if elected, setting up a potential showdown in the early stages of the new leader's time in office.

On Monday, criminal barristers will go on strike over legal aid funding, and an already lengthy backlog of cases in the courts will grow longer. And extensive industrial action is expected in other sectors, with disruption of port, mail and telecoms services and potential strikes from rail workers, teachers, nurses and civil servants. 

Health services are also under considerable strain, with significant delays in treatment. The National Health Service is in "the most serious crisis in its history," according to Jeremy Hunt, the former health secretary.

3. Brexit and foreign policy

Brexit wasn't over in 2016, when the UK voted to leave the EU; it wasn't over in 2020, when the country finally left the bloc, and the fallout from it continues to reverberate across British politics.

UK-EU relations have been tetchy in recent months, and the situation could soon become more strained if Truss moves to trigger Article 16 of the Northern Ireland protocol, which would suspend some of rules regulating trade in the region.

Both Truss and Sunak have committed to legislation that would unilaterally rewrite the protocol, a move the EU angrily opposes and that could lead to a trade war. Any attempt to remove the UK from the European Court of Human Rights would also add to friction with the EU.

The conflict in Ukraine is another potential headache, with Britain strongly backing Kyiv with rhetoric and weapons in the ongoing conflict. 

Truss is a particularly vocal supporter of Ukraine, but with the cost of living crisis building across Europe and elections due in the United States, there are questions over the extent to which Western support will continue.

4. National and party disunity

The new prime minister will be under pressure to try to reunite the Conservative Party after a campaign punctuated by aggressive briefings between the two candidates that exposed internal divisions. 

Truss, in particular, could face a fight to win over lawmakers after getting the backing of less than a third of Conservative MPs in the first phase of the leadership election. While the party holds a strong majority on paper in the House of Commons, the splits within it mean the leader will be able to take nothing for granted. 

Weekend reports suggest that if she wins, Truss will name her neighbor, Kwasi Kwarteng, as chancellor of the exchequer, close ally James Cleverly as foreign secretary and right-wing favorite Suella Braverman as home secretary. She is also being urged to name Sunak supporters in her top team.

Another potential flashpoint is a parliamentary inquiry into whether Boris Johnson deliberately misled parliament during the "partygate" episode, which could lead to his suspension or removal from parliament. The new prime minister won't have the direct power to stop the inquiry, but some of Truss' supporters are backing a parliamentary motion calling for the investigation to end.

Uniting the country will also be a daunting task. Scotland is pushing for a new independence referendum, a power-sharing government in Northern Ireland has not been resumed, and YouGov polling suggests voters are losing faith in the system – just 6 percent believe their views are the main influences behind government decisions.

While Sunak's ratings in August were relatively stable, approval of Truss dropped markedly with people who voted Conservative in 2019, according to Opinium, and the Conservatives consistently trail the opposition Labour Party in national polls.