Arthur Balfour
Arthur James Balfour, 1st Earl of Balfour KG OM PC DL was a British Conservative politician and statesman.
He took up the job when Lord Salisbury resigned in July 1902. Salisbury was his uncle, and there were some accusations that Balfour had got started on the political ladder through nepotism, hence the Stock British Phrase "Bob's Your Uncle" (Salisbury's full name was Robert Gascoyne-Cecil, 3rd Marquess of Salisbury).
Practically the first thing Balfour had to do as Prime Minister was the Coronation of Edward VII and deal with the end of the South African War.
And for a while it was all peachy. The Liberal Party was still a mess over what to do in South Africa. His two biggest acts where a new Education Act and Irish Land Purchase Act, letting the Exchequer loan money to Irish tenants to buy land. He also created the Committee on Imperial Defence.
He also presided over a dramatic improvement in relations with France, ending in the Entente Cordiale of 1904, and almost got involved in Russo-Japanese war, although most of this was down to his Foreign Secretary.
His budget caused dissension however and was one of the prime causes of a rift that grew in his party, with his opponents wanting a more protectionist and less welfare focused approach.
Eventually he agreed to meet them half way, putting in place equal tariffs against foreign powers when they placed tariffs on British goods.
However, you try and please both sides, you risk annoying both and that is what he did. His authority was slowly drained away and a lot of people jumped ship, including one young MP known as Winston Churchill. (Churchill himself would later say "If you wanted nothing done, Arthur Balfour was the best man for the task. There was no equal to him").
In 1905 he resigned as Prime Minister in an attempt to give his successor the chance to form a worthwhile government. This did not happen and at the election Arthur Balfour lost his seat. While he later gained another, it was the end of his time at the top.