The UK takes over the rotating presidency of the European Union on 1 July for six months.
The BBC News website explains what the job entails, and sketches what the UK hopes to achieve.
What is the presidency of the European Union?
We are actually talking here about the presidency of the Council of the European Union, which is one of the three most important EU institutions.
The others are the European Commission, and the European Parliament, which have their own presidents.
The Council brings together ministers from member states' governments.
6-8 July: G8 summit
August: New bid to get Iran to give up uranium enrichment
5 Sep: EU-China summit
7 Sep: EU-India summit
14-16 Sep; Millennium Development Summit
4 Oct: EU-Russia summit
17-21 Oct: EU-Ukraine summit
27-28 Oct: European Council
24 Nov: EU-Canada summit
28 Nov - 9 Dec: Climate change conference, Montreal
13-18 Dec: WTO ministerial meeting, Hong Kong
15-16 Dec: European Council
Officially, the title "President of the Council" refers to the foreign minister of the country holding the EU presidency, though it is sometimes applied to the head of state or government.
One of its main tasks is to approve or reject, together with the Parliament, laws put forward by the Commission.
Each country in turn holds the presidency for six months. The UK follows Ireland and the Netherlands (in 2004), and Luxembourg, whose presidency ends on 30 June. It will be followed in 2005 by Austria, and then Finland.
The UK's agenda flows from a strategic programme for 2004-6 agreed jointly by all these presidencies.
What is the role of the presidency?
It organises the work of the Council and the dozens of committees that prepare the ground for agreements to be made when the ministers meet.
Where there are disagreements, it is the presidency's job to search for compromise.
The presidency also organises and chairs two summits, known as European Councils, where heads of state and government set general political guidelines for the EU's development. These will fall in October and December.
What are the main priorities for the British presidency?
The task of securing agreement on a framework budget for 2007-2013 falls to Britain after the failure of the Brussels summit on 16 and 17 June.
The UK also has to deal with the continuing fallout from the rejection of the EU constitution by voters in France and the Netherlands.
It will be arguing that the priority is to make the EU's economy more competitive, by cutting red tape and liberalising the economy.
Britain also wants to ensure that negotiations with Turkey on its possible accession to the EU begin as planned on 3 October.
What are the chances of success in these priority areas?
A deal on the budget is highly unlikely, though Prime Minister Tony Blair has said he will try hard to get one.
The problems include the bitterness of the rows in Brussels, which have left a legacy of bad blood, and the difficulty for the UK in playing the role of honest broker when its own budget rebate is one of the main sticking points.
The UK will also find it difficult to score dramatic successes on the economic liberalisation front.
This is primarily an area for national rather than European legislation. A key EU directive designed to open up the European market in services, is likely to face stiff French opposition.
So the most the UK can realistically achieve is to kick off a debate that may bear fruit in the future.
Another difficulty for the UK is that opposition to Turkish membership of the EU has increased since the referendums in France and the Netherlands.
Some argue that these votes were, in part, votes against EU enlargement, and that the EU should stop and take note of voters' concerns.
What else is on the presidency agenda?
There is a long and varied list. Here are a few items:
Climate change: Exploring options for reducing greenhouse gas emissions after 2012, when the Kyoto protocol will have run its course. An effort may also be made to bring aircraft emissions into the EU emissions trading scheme.
Aid to Africa: The UK will represent the EU at the UN Millennium Summit in September. The EU has already agreed to double aid to Africa. After the summit, the UK wants to shape a "comprehensive and long-term global strategy towards Africa".
Better regulation: The UK wants to improve consultation with business on new EU legislation, and to strengthen impact assessments that make sure the benefits of EU laws outweigh their costs. It also wants to cut red tape.
World trade: The aim here is to ensure that a WTO ministerial meeting in December takes steps to improve developing countries' access to markets. Before the meeting, the UK will support measures to reform the EU's system of sugar subsidies.
Chemicals legislation: The long-awaited European directive on the safety of chemicals gets its first reading in the last quarter of 2005. The UK government wants to help make sure it is good for public health, the environment - and business competitiveness.
Counter-terrorism: The two big goals here are agreements on the European evidence warrant - which will ensure evidence gathered by one member state is recognised in others - and on long-term retention of telecoms data (such as records of telephone calls made from a given number).
What are the biggest headaches for the UK presidency?
Experts say it is possible that French President Jacques Chirac will attempt to undermine the British presidency, either out of long-standing rivalry or anger over the UK's stand at the Brussels summit in June.
Germany presents a different problem: German leaders are unable to take big decisions until a new government has been formed, in the wake of the 18 September election, leaving the UK with a lot of work to do at the end of its presidency in November and December.
Instead of the usual European Council summit in October, the UK has scheduled an informal meeting, where leaders will meet to discuss social and economic reform without the usual pressure of having to sign up to a list of agreements.
What are the big international events of the presidency?
In August, Britain, France and Germany are meant to put new proposals to Iran in the hope of persuading it to suspend activities related to uranium enrichment.
If, as expected, Iran rejects them, there could be tension between the EU and the US over what to do next, with the EU keen to prevent any military response.
Apart from the Millennium Development Summit in September and the World Trade Organization ministerial meeting in Hong Kong in December, there is also a major UN conference on climate change starting at the end of November.
The UK will present to this conference any agreed EU position on emissions reduction in the post-2012 era, when the Kyoto Protocol will have run its course.
There will also be EU summits with China and India in September, Russia and Ukraine in October, and Canada in November.
The final European Council of the presidency takes place on 15 and 16 December in Brussels.